This is what you might call the polite TERF argument. Trans folk of all genders already know where the knives are in this rhetoric, but for the rest of you, let's talk... 
"I support trans rights" and "trans women are actually men in dresses" are incompatible claims. The belief that trans people are not who we say we are, that an unscientific biologism chains us to a patriarchal birth assignment, is *the* rationale for discriminating against us.
Secondly, arguments that try to slyly define sex in this way were repudiated long ago by no less than a radical feminist than Catharine MacKinnon (who'd, lamentably, agree with these types on the need to oppress sex workers--she's a rare SWERF who's not a TERF).
In short, MacKinnon argued that biological explanations for patriarchy (and that is what this is) presuppose what they need to explain. *Why* does a certain, perceived bodily configuration lead to oppression? Because it does, says the TERF.
"Gender refers to the cultural norms associated with biological sex"--no, it doesn't. At best, they're associated with a *perception* of it, and that's certainly not a cultural universal.
TERFs, for reasons of ideology, religion, or prejudice, get the order of operations the wrong way around. Sex does not cause gender to be perceived a certain way; it's the inverse, and trans people demonstrate that clearly.
That "nice TERF" I cited goes on to, predictably, claim trans women do not experience misogyny; that's a flat out lie, of course. We're paid less, sexually harassed, raped, talked over, stalked, experience domestic violence and male entitlement, on and on. You (should) know that.
And that all happens because of the fact that we're *perceived* be a certain gender/sex complex. Such antagonists don't check our bits, or our birth certs, or our karyotypes. We code as "woman," because we exist, sociologically, as women. That matters most.
Whether trans women are read as women, or read as trans, patriarchy will do its thing to us. At a certain point it becomes indistinct.
The man who wouldn't leave me alone when I was getting my hair done, harassed me, followed me out, and demanded a blow job, could've been a chaser. Or he might not have been. The end result was the same: entitlement to my body, a threat to my safety.
Did that young boy in Hadley, MA who shouted "nice legs, baby, when do they open?" at me out his car window read me as trans or as a cis woman? It hardly matters, after a point. It does the same work, establishes the same dominance and fear.
But I suppose the ultimate existential proof comes from TERFs themselves, who demand that trans women must prove we're women by stripping off and showing our scars, proving our womanhood by proving our holy suffering. So lurid, perverted a demand would never be made of a man.
