Situation: there is a discussion in the office about making a decision. You make a valid argument based on facts, and the other person, usually a manager, replies with:

"I don't like your tone"
or
"I don't like your attitude"

This shifts the focus of the conversation from the facts being discussed to the tone or attitude; the other person, instead of defending a weak position, forces you to defend your tone or attitude.

I have seen this enough times to know that it's a general and common problem.
The question is: how to avoid having a discussion with a manager being derailed by "I don't like your tone"?

The wanted outcome, of course, would be having your argument handled as intended, with numbers and facts being considered to the logical decision you are supporting.

Edit: for clarity, in this situation facts and numbers have been listee without attacking anybody.

The actual best way to "counter" someone criticising your tone is to try to avoid having them do so in the first place, by avoiding the problematic tone.

What's written below applies to after they've criticised your tone, but a lot of it (specifically the "rephrase" part) would also help with avoiding a tone that may offend others.

Step 1: Apologise

This may not be the advice you're looking for, and you may not believe you've done anything wrong (and this may be true). But it would still be the best way to deescalate the situation.

It doesn't have to be a particularly complex apology. Simply saying "sorry" and pausing for a few seconds could work well enough.

Step 2:

From here you have a couple of options:

Drop it

Think what you're actually hoping to achieve in this discussion, how likely it is to happen (especially considering how reasonable you believe they are, and whether they even have the power to change the decision) and whether you have anything more to say or whether you'd just be going in circles.

If you're criticising a decision, but you don't have a good alternative, or you're simply being told about a decision that's already been made, there may be little that can be gained from trying to change their mind.

Some points I've made below may also lead you to dropping it.

Delay or move the discussion

This is probably the best way to continue the discussion if you really need to (which may not be true) and you're unable to rephrase what you've already said in a "better" way.

You could say something along the lines of "Can we continue this discussion tomorrow? I need to spend some time thinking about it and getting my thoughts in order".

You could, as another answer suggests, move the discussion to email instead. Or you could invite some other people to join the discussion (although be cautious with this, as it may be seen as an attempt to embarrass them or undermine their authority).

Rephrase what you've said, or take a different approach

Following on from step 1 with "what I meant to say was" could be a good way to transition.

This is probably the most difficult option if you don't know what the problem with your tone was. It's also difficult to give specific advice for - it would be much easier to answer this for a specific scenario. However, there are a couple of things that it might help to keep in mind:

• 
  

  How you said something is often more important than what you say

  
  
  

  The world may be simpler for some of us if everyone were logical and could look at the facts presented without being swayed by how they were presented. The world unfortunately just doesn't work like this.

  
  
  

  How you say things is very important.

  
  
  

  I feel this is especially relevant considering you say you used a logical argument with numbers and facts, yet you say nothing about the tone with which you said this.

  
  


• 
  

  Tone is subjective

  
  
  

  You may believe your tone is fine. If other people have a problem with it, they're not any more right than you are. But then you would be faced with the choice to either try to improve your tone or just live with the fact that interacting with those people will be difficult.

  
  


• 
  

  It's not "you versus them"

  
  
  

  You're not trying to (or shouldn't be trying to) "win" the argument. You're trying to help them see the error in their ways, or work together to find the solution that's best for the company, or whatever else.

  
  


• 
  

  Compromise is good

  
  
  

  Some arguments are simply not worth having (or continuing). In some cases you may not be able to convince them, in other cases the difference between the end results would be negligible when looking at the bigger picture.

  
  
  

  It doesn't matter who's "right" if you're just wasting time.

  
  


• 
  

  They are your manager

  
  
  

  They are the decision maker. If they want to make a terrible decision, you can, and should, try to guide them in another direction, but ultimately it is their decision to make. Even if this ends up ruining the company, or they end up blaming you, it's still their decision to make, and it's still not your place to try to stop them after they've made up their mind. Well, you could try to go above their head, but that's a whole other question (and generally won't go well). Or you could decide to find another job if their decisions are that bad.

  
  
  

  The above may not apply to exactly as is to every situation, but understanding your place and keeping that in mind should put the discussion into proper context. It's more you giving them some information or perspective they might be missing, and less a discussion among equals where they need to defend their point (actually every discussion, regardless of with whom, is likely to go better if you approach it from the former point of view instead of the latter).

  
  


• 
  

  Dismissing is bad

  
  
  

  You do not ever want to say something along the lines of "that's a terrible idea" or "you're wrong". It's generally more constructive to just remove these statements and, if applicable, just stick to the part where you justify this instead.

  
  


• 
  

  Questioning is better

  
  
  

  If you think something is a bad idea, you can ask questions to lead them to reach the same conclusion, or their answers could reveal some information which changes your mind instead.

  
  
  

  A simple "have you considered using X instead" would be much more productive than "using X would be so much better".

  
  


• 
  

  Avoid too strong statements

  
  
  

  If they might have some personal investment in what you're directly or indirectly criticising, it might be best to downplay it. For example, instead of "users absolutely hated it", you could say "users were not at all fond of it". You could even ease up on that more by dropping the "at all" (whether this makes sense heavily depends on the message you're trying to send and how core this is to your argument).

  
  

Note: There may be people who "don't like your tone" simply because you question or disagree with them in any way, shape or form. In this case you'd strongly want to tend towards dropping it, and just avoiding questioning or disagreeing with them wherever possible (while also looking for another job). Although in my experience these people are very much in the minority.

Since, as you say, meta discussion about tone or attitude distracts from the important facts, opinions, and speculations that are part of any business discussion, you should keep your tone and attitude neutral-to-friendly at all times. Should you mess up on this to the extent that a coworker needs to say "I don't like your tone" you need to fix this by saying something like:

I'm sorry. I didn't mean to bring emotions into this or upset you. I appreciate you letting me know that I am over the line.

Then take a deep breath. Get calm. Now, restate your point - your facts - calmly. If this happens a lot, you can use a shorter version of the apology before restating.

For example:

Any idiot can see the only safe way will be to use two factor authorization!

I don't like your tone.

Ah, sorry, thanks. [Pause.] Two factor authorization will be much safer. I think considering what we're protecting, it's the way to go.

You don't need to back down from your position, including any facts it contains, but you can state it in a way that doesn't offend any one. This will make it more likely that people will agree with it, so over time you should become truly grateful to the people who are helping to lead you to a more neutral-to-friendly way of speaking.

First, ensure that the comment is not appropriate. At times, we choose to use a tone (knowingly or unknowingly) that may not be welcome by all alike. So, first eliminate the possibility that they are complaining about a valid problem.

As we say "Before you try to get into an argument with a fool, make sure they are not doing the same".

However, if your boss / manager is trying to dismiss you / your valid argument using that as an excuse, the best way to counter is to not allow them that chance. The moment they bring up that argument, you stop conversing and say something like:

"I'm going to put my comments / proposals in an email and going to share with you. Once you have reviewed it, let me know your comments"

This way, you can avoid the whole point behind that diversion.

@Duekling's answer is spot on in terms of what to do in the aftermath.

Additionally, I would recommend some careful introspection about the situation and what you said.

When you say that "facts and logic" are on your side, how can you be sure?

First, there's the problem of whether or not you have all the facts or just some facts. People often inadvertently cherry-pick the facts they want when building a case for their argument, or worse, they're unaware of other information-- "unknown unknowns".

Secondly, there's the problem of differing value systems. You might be in possession of the facts but aren't weighing them the same as the other person. Does that mean one or the other is "right"? That's necessarily and intrinsically subjective.

Finally, assuming you're "right", there's the matter of "loss of face". NO ONE enjoys being proven wrong in a scenario where they're being observed and judged (in this case by management or peers). To them it feels like they're being blindsided and there's often a backlash for you as you may have observed.

In business, people often call meetings to "make decisions". I have found that those of us from STEM backgrounds tend to take that literally and assume that the purpose of a meeting like that is to hash stuff out, disagree, and reach consensus through reasonable arguments. In most places that is not the actual purpose of such meetings and you're setting yourself up for serious problems that will look like office politics if you openly challenge someone in such a meeting. What you need to do is to adapt yourself to the way decisions are made in such an org. That could mean doing some serious 1-on-1 discussions with others who you disagree with to gain consensus well in advance of that meeting. That way, even if there is actual disagreement, you are not blindsiding anyone and there's an opportunity for each side to address the other side's point of view rather than just making them "right" or "wrong".