Your cognition (thought process) or behaviour can be wrong but what you are feeling is always right. You have to separate what they are feeling with how they are thinking or how they are behaving.
In terms of dealing with this I have a principle of "validate and then direct"
The most important thing is to validate their emotions and only when their emotions is validated then direct, correct or lead with practical solutions afterwards after they have calm down.
Even if they are angry at you for completely unreasonable or illogical way
You still say "I can see you are upset and I can see how you can interpret things that way." Only after you validate then you can then say "however my intentions was x, y, z" when explaining what you really meant.
This doesn't mean you can't set limits if people are behaving unreasonable to you. It's just that you validate first and then set limits. You are essentially separating how they are feeling with how they are behaving ie "I can see that you are angry. I know that things have been stressful or tough recently. However I need you to stop shouting so that we can speak about your distress in a calm manner"
So essentially the person has the right to be angry. They just don't have the right to be shouting/aggressive or disrespectful/insulting etc.
So yes you can point out irrationality/over-reaction as long as what they are feeling is perceived to be respected and being understood.