There are a surprising number of tr*ns*ndr*ph*b*a advocates who will concede that transmisogyny is a more severe oppression, but still insist that they just want a word to describe the oppression they face, even if it is lesser. If they are told "your oppression is called transphobia" they generally get frustrated, because they think we're not acknowledging all the shit they have to deal with. I think there's an underlying problem here, that they simply don't understand what we mean by "transphobia".
I think a lot of them would define "transphobia" as something like "the belief that your gender is your AGAB", or "the denial that you are the gender you say you are", i.e. primarily misgendering, and everything that follows from misgendering like bathroom bans. But they have observed that they are not merely misgendered: masculine gender presentation in those assigned female is actively punished by society, which will go out of its way to make them revert to a feminine gender presentation. To them that's not just transphobia, because they are not just being misgendered as cis women, but actually being treated worse than cis women. Thus: tr*ns*ndr*ph*b*a, a hatred of masculinity in those who were assigned female.
The only problem is, that is not how we would define "transphobia". Transphobia is not simply a truth claim about what your gender is, but rather a moral claim about what it ought to be: it's the belief that your gender presentation should not deviate from your AGAB. It's the belief in birth assignment as a social contract that is violated by gender nonconformity and totally torn up by transition. Transphobia is a force that punishes gender deviance in the hope of preventing it.
Any of the classic examples of tr*ns*ndr*ph*b*a, such as being denied access to medical transition on the basis that it will "ruin your pretty female body", are straightforwardly transphobia. It's not about masculinity being hated specifically, masculinity is hated for you, femininity is hated for me, that's just what transphobia means.
The reason we needed a word for "transmisogyny" is because the kinds of punishments transphobia doles out to transfems end up being significantly harsher than those it gives to transmascs, and that word is simply the name given to that gulf in our experiences. "Transmisogyny" is the observation that transphobia harms us more than it harms you, it cannot coexist with tr*ns*ndr*ph*b*a because its whole reason for existence is that gulf. We can't both be treated worse by transphobia than each other.
It seems to me that tr*ns*ndr*ph*b*a advocates often regard "transphobia" as a fairly minor oppression, essentially just misgendering, on top of which sit two other much bigger oppressions, the hatred of femininity in those assigned male, and the hatred of masculinity in those assigned female. This seems a natural taxonomy to them. The idea that all three of these things are actually the same thing is not one that they recognise, unless as an umbrella term with these constituent parts as separate oppressions beneath it.
So, is there actually any reason to choose the transfeminist framing over the tr*ns*ndr*ph*b*a advocates' framing? I think there is, for two reasons:
Defining transphobia as essentially a belief that gender = AGAB is a really bad definition, because it's a belief that no one actually holds. When people misgender trans women as "men" they do not really believe we are men (which is obvious when you look at how they treat us), they are calling us that as a punishment, not as a genuinely-held belief. To them we are not men but T-slurs. Transphobia is far better understood as a punishment for breaking a social contract, a whole host of different ways of pressuring us to conform to our AGAB, or if that is not possible, eliminating us.
Having a specific oppression name for the fact that masculinity is hated in those assigned female is a framing that focuses attention in the wrong place imo. It is not about masculinity specifically, it is about gender deviance generally. The logic of why transphobia is more severe against transfems (transmisogyny) is that masculinity is actually generally considered superior to femininity. Having an oppression that can be characterised as "hatred of masculinity" comes across as reactionary, since it is a reversal of what is globally true. This is why the tr*ns*ndr*ph*b*a movement can so easily become a broader men's rights movement, because the founding principle of it is a supposed societal hatred of masculinity, when what society is actually hating is gender deviance, and in fact, if you have to be gender deviant, society would much rather you be masculine.
I'm sure people will say I'm giving tr*ns*ndr*ph*b*a advocates too much benefit-of-the-doubt here. I know that a lot of them simply do hold the reactionary belief that masculinity is hated by society, and especially in queer or progressive groups, a belief that is a total inversion of what the world is actually like. And I recognise a lot of thought patterns in common between tr*ns*ndr*ph*b*a advocates and the men's rights advocates of a decade ago. But I think it's still important to try to drill down into the philosophical differences between us, because I know there are some of them who see themselves as supporters of transfeminism, and are frustrated with what they see as our refusal to acknowledge their suffering, a frustration that is ultimately based simply in a misunderstanding of how we define things.