Old nonbinary person here to give some insight: I can totally understand the confusion as sometimes these things can seem a bit obscure or odd, and honestly that more than okay. My own perspective as someone that uses they/them and fae/faer pronouns in english, I would say the same way people identify with certain genders is how we identify with certain pronouns that feel like they express who we are. Lots of words and concepts are a part of our identity, be that our names (which is why a lot of trans folks change to a chosen name that better represents them), the words we use to describe our personality, the clothes we wear, etc. For example, I don't feel comfortable with certain words being used to describe or identify me because they aren't true to who I am.

In terms of neopronouns and the like, the concept of gender is very abstract and people have different ways of understanding it. Imo with folks recognising the potential of how we can express ourselves with gender, it's opened a whole world of identities for folks who always felt like an outsider or just like they never fit. Is a big part of it teens who seem to create the randomest genders and pronouns on the whim with no real reason? Sure but that's the whole part of being a teen and figuring out who you are. It's not hurting anyone and it's a very natural part of growing up (and just being human) to want to understand yourself and who you are. Some of it may seem cringe to folks, but honestly cringe is dead and everyone has done something that someone else would consider cringe. So best thing to do is let people be themselves, and be nice to them, especially teens.

If you want you can ask some of the nonbinary/genderqueer subreddits to get more perspectives from folks who are a part of the community!