Rational people are systems of ideas that can temporarily remove any one idea in the system without losing identity. We can remain functional without any one idea. This means we can update or replace it. And in fact we can often change a lot of ideas at once (how many depends in part on which).
To criticize one idea is not to criticize my rationality, or my ability to create knowledge, or my ability to make progress. It doesn't criticize what makes me human, nor anything permanent about me. So I have no reason to mind it. Either I will decide it is correct, and change (and if I don't understand how to change, then no one has reason to fault me for not changing yet), or decide it is incorrect and learn something from considering it.
The way ideas die in our place is that we change ourselves, while retaining our identity (i.e., we don't die), but the idea gets abandoned and does die.