It is true that most copper IUDs aren't hormonal IUDs (but all those side-affects I list still apply), but that is not my point of contention with your post.
I still think it is completely misplaced for any man to bring up the subject of invasive, semi-permanent female contraception. The issue here is not the matter of discussing contraception in general terms, but - I'll repeat - invasive, semi-permanent female contraception. Particularly with strangers, in this case someone much younger. Perhaps you do not hear how offensive that is, or notice how your response and lack of apology indicates a seemingly willing blindness about it.
I've said all I have to say on the matter, really. Matters of procreation and contraception are not equal, the implications for men are not the same and your 'mansplaining' is not welcome. It comes across as oppressive, insensitive, to jump to something invasive and semi-permanent coming from a male.