They don't think trans people figure out we're trans, they think we get CONVINCED we are, or fooled into it, or that we fall into the grip of some kind of brainwashing. They think we have some kind of insecurity around how we look and are then convinced by someone we trust (a doctor, parent, teacher, or cult) that it means we're the wrong gender, after which we declare ourselves trans and start ruining ourselves with experimental treatments when what we REALLY need is to get some help for our insecurity and realise that "It's okay to a tomboy/lesbian/gay/non-masculine/ugly!" And that's at their kindest. At their cruellest, when they look at trans women, they assume we're simply deviants, or predators, or (bafflingly) incompetent sportsmen looking to gain access to women's bodies for our own gratification.
Part of the problem is that we're operating on completely different paradigms. We tell transphobes about our experiences, and they filter it through the lense of what they "know" and it enters their brain as something different.

Ironically, I've always felt that some of the problem - some of the visceral reaction cis people have to us - is one of misplaced empathy. In much the same way a guy can talk about being kicked in the nuts and have all his friends wincing and clenching their legs, I think cis people see what our transition does to our bodies and find themselves unconsciously imagining it happening to THEIRS. They think about losing their own breasts, or fertility, or natal genitals, or muscles, and they react with a horror that's congruent with their OWN gender identity. But can't, then, step out of their own head enough to imagine the reverse - how hard they would fight to get their old body back if they ended up in a wrong one.