Some of these might work better for somewhat shy (yet inquisitive) teenager:
"Why do you need to know? Does it matter? Will you treat me differently depending on what I tell you?"
"I don't know, what do you think?" then "Why do you think so?"
"I need to think about it. Do I have to tell you now? It's rather private, no?"
Etc.
Basically, bounce back the question with more not-so-naive questions (ideally tailored to gently highlight some of the darker aspects of genderism: the prejudices, the hollowness, the inconsistencies, ...)
May need to think about precisely what to say if the pronoun-worshipper goes on a strong "everybody must share their pronouns so that trans people feel included" rant (which implies not sharing yours is "transphobic")
I think this one very much depends on the group of people involved, their relationships and personalities, and whether bridge-burning is an option.
A somewhat neutral deflection would be to invite the person standing on their soapbox to explain further what their pronouns are and what it means to them, etc., and let them rant till they've ran out of steam. You can keep them going quite a while by rephrasing what they've said and politely ask if you got it right. The internal contradictions are likely to wear them out sooner or later.
If they still insist on hearing your pronouns near the end, you can just conclude by thanking them and saying they gave you lots to think about, and not to worry, any pronouns should do for now.
... Let's face it, no one is really interested in hearing about other people's pronouns, they just want an excuse to talk about theirs.