It's absolutely nothing like it at all. "Him" is not a derogatory word.
It is to someone who has spent years or even decades not wanting to be a 'him'.
It's about context. Just like there's a difference between accidentally using the wrong pronoun, and insisting that you call someone a man or woman because you assert your knowledge of biology trumps theirs.
There are neurological and hormonal factors that cause transgenderism. Those are just as biological as chromosomes and dangly bits. Just because biology doesn't always play by the rules we think we've discovered doesn't make it less biological.
I'd say that the fact transgender people exist, and cannot change their gender identity is just as objective and/or arbitrary as judging chromosomes or 'looking' male or female.
Not until the transition, they aren't. The difference between our positions should be obvious: you just ask them what they feel like; I rely on more objective measures.
But you were talking about biological truth. And this is not some kind of rhetorical trick, I'm genuinely interested... Why does this transition matter to you? It seems a little arbitrary to me to on the one hand define genders by the biological definitions of chromosomes, birth sex, and so on, and at the same time accept that hormonal and surgical alterations can change it 'enough' to warrant a different pronoun.
Especially in everyday situations, which is where these questions about how to address someone arise.
I don't think I could reliably judge by looking at someone whether they are an unusual looking 'regular' man or woman, trans, pre- or post-op, what kinds of surgeries they have had or are planning on having, if they're on hormones, and whether or not that meets certain criteria. And I am not going to ask them about any of that in order to decide which pronoun I'm going to use.