"Would trans people exist if we didn't have gender as a social structure?" is a big one. It's even been asked here.
It's just such a pointless question that is functionally designed to discredit the trans experience. "Your existence is only a thing because of the way our culture is, and is therefore invalid", is basically what they are trying to say.
It also makes little sense because there are other cultures which have more than two genders (both currently and historically). Basically, humans as a species have been trying to explain trans people for thousands of years, and have mostly been unsuccessful.
Most of the questions that I hate getting are the ones that are leading - people with a little bit of information and a whole lot of opinion who want to tell me how wrong I am for being trans, or want to create a "gotcha" moment. Like, Yes, i did in fact decide to play my life on Hard Mode and decided to be trans - Like, come on, really? I don't have all the answers because science doesn't have all the answers either - no one does so far as we can tell - but that doesn't mean that I can be dismissed because I make your life inconvenient (the plural you, not you specifically).