I think “clicky” people are people who are not emotionally vested in their beliefs.
Many people need their beliefs to be true in order to feel like they are valuable and worthwhile people.
Clicky people simply don’t need that (or at least need that to a lesser extent). Instead, clicky people need to be right whether or not that means they were initially wrong.
Actually, I believe the question was “would you not describe yourself as athiest/agnostic” rather than “identify as” which is a very different question.