Because it’s reassigning someone’s gender - e.g. making a female body look more like a man’s. We don’t have the technology to change someone’s biological sex, but we can help them by giving them a body that more closely resembles their gender identity.

Because you can't surgically change someone's sex; or do you think that eg. trans women have wombs? Here's how the Canadian Institutes of Health Research explains the difference:

Sex refers to a set of biological attributes in humans and animals. It is primarily associated with physical and physiological features including chromosomes, gene expression, hormone levels and function, and reproductive/sexual anatomy. Sex is usually categorized as female or male but there is variation in the biological attributes that comprise sex and how those attributes are expressed.

Gender refers to the socially constructed roles, behaviours, expressions and identities of girls, women, boys, men, and gender diverse people. It influences how people perceive themselves and each other, how they act and interact, and the distribution of power and resources in society. Gender identity is not confined to a binary (girl/woman, boy/man) nor is it static; it exists along a continuum and can change over time. There is considerable diversity in how individuals and groups understand, experience and express gender through the roles they take on, the expectations placed on them, relations with others and the complex ways that gender is institutionalized in society.

Yeah, sure, a pedant could argue that "gender correction surgery" is the wrong term since gender is a social construct and that's not what's literally done in the operation, because the operation is more about correcting (ie into accordance with whatever that person's gender is) external "markers" of sex and/or genitals, but that doesn't mean sex reassignment is therefore the correct term.

Because we don't. The old name was "Sex Reassignment Surgery" (SRS), but the new names are "Gender Affirming Surgery" and "Gender Confirmation Surgery".

Few trans people have bottom surgery. It’s horribly invasive and painful.

The whole situation is BS in the first place, back in the days the concept of gender was introduced to allow some flexibility in the social aspects while keeping sex (as in phenotype) a binary which science already knew it wasn't. Bimodal distribution, yes, binary, no. Things get complicated fast once you go past egg cells and sperm, that's the only actual binary that exists.

English in particular uses transsexual because back in the days activists wanted to avoid associations with sexuality, to not get tangled up in people's homophobic sentiments. Other language use precisely that term, transsexual. Hirschfeld coined "transvestite", back then a catch-all term for behaviour not conforming to your sex assigned at birth (and you could get a transvestite pass in Imperial Germany to stop the police harassing you for "inciting public disorder"), Benjamin coined "transsexual", in English, as a diagnosis separate to "just liking to dress up differently", it got replaced later on don't ask me for a source right now.

penis reassignment surgery (PRS)