TRANS EXCLUSIONARY RADICAL FEMINISM
If you ask a TERF what the "radical" in "radical feminism" means, chances are she will tell you that it refers to locating the root cause of women's oppression in their belonging to a "sex class"* that is subjugated under patriarchy for the sake of controlling their reproductive capacity ("radical" being used in the sense of "pertaining to the root").
(*not all TERFs use "sex class" terminology, but the structure of the arguments being made is largely identical.)
The "trans exclusionary" part refers to trans women being excluded from the scope of the analysis that this kind of feminism offers on account of not belonging to the "sex class" whose reproductive capacity (i.e. the ability to bear children) is being controlled.
"Trans Exclusionary Radical Feminism", for as long as that term has existed, has never "excluded" all trans people from its analysis. It has always "included" transmasculine people (whose gender is usually disregarded and disrespected by its proponents) as "belonging to the sex class" whose reproductive capacity is being controlled. TERFs have used the expression "You can't identify your way out of oppression" illustrating this idea to the point of it becoming a cliche.
That isn't to say that TERFs necessarily like transmasculine people: The charge of pursuing an individual solution to a structural problem - that trans men are "members of the female sex class trying to escape their oppression" through misguided means, that trans men are simply trying to change their location from oppressed to oppressor while leaving the oppressive structure intact - has been frequently directed at transmasculine people.
This accusation, however, is only one of attempting to do so: TERFs do not believe that it's actually possible to escape "sex based oppression" by way of transitioning or any other individual action. They do not believe that transmasculine people are granted a position that allows them to benefit from "sex based oppression" as they do not believe patriarchy allows "women" to escape their "sex class".
The account that TERFs offer of transfems' plight under patriarchy is simply that they are facing a secondary oppression as "gender non conforming males" for subverting the gender roles assigned to them on the basis of their "sex class" as "males". According to TERF analysis, trans women are not oppressed on the basis of their womanhood because the oppression of women is "sex based oppression" aimed at controlling the reproductive capacity of the "female sex class".
The charge that TERFs make against trans women (which serves as the basis for excluding them from feminist organizing) is that they are infiltrating and derailing/subverting feminism. Trans women are thought to be "males" (biologically, physically, socially, psychologically etc.) whose interests are not aligned with those of the "female sex class" but with those of the "male sex class" and who will therefore divert the goals of feminism away from the liberation of the "female sex class" if granted the right to participate in the formulation of feminist agendas.
The actual interests of transmasculine people are thought by TERFs to align with the liberation of the "female sex class" so they see no reason to exclude them from feminist organizing. At most, transmasculine people are thought of as having a "false consciousness" and being mistaken about what is and isn't in their interest on account of identifying with an oppressor class they are not actually a part of.
Do TERFs hate men? That depends on what is meant by "hate" and "men". To TERFs "men" means "members of the male sex class" (cis men, transfems) and doesn't include trans men (whom they view as "women"/"members of the female sex class"). TERFs believe that "men" have structural power over "women" based on these sex classes. They believe that there are coherent class interests that unite the members of each "sex class". How they actually "feel" about "men" is somewhat variable and ranges from relatively neutral academic analyses viewing them as an oppressor class to ascribing them more or less demonic essential characteristics.
Trans women aren't seen like other "men" by TERFs though: They are conceptualized (in explicitly conspiratorial terms) as something like the storm troopers of patriarchy - an especially militant advance force (possibly giving up their humanity and becoming a kind of medically constructed monstrosity) to strike at the core of feminism with the goal of hollowing it out and clearing the path for "colonizing" and resorbing it into the patriarchal mainstream. Trans women are understood as an especially nefarious category of person because they are seen as posing a direct threat to the ability of "women as a sex class" to organize among themselves, to develop and use the language and theory they need to understand their own oppression and thereby resist patriarchy and bring about their liberation. Trans women are not just seen as attackers of "female safe spaces", they are seen as the attack itself. Their very existence is made out to be a stratagem devised against feminism and "women".
How and why the "sex class interests" of transfems supposedly align with those of "men" is never quite explained in materialist terms. In this point, TERFs invariably have to fall back on idealist concepts like biological determinism, spiritual essence, socialization, etc. Whereas transmasculine people are seen as having a "false consciousness" for mistaking where their material interests lie, the question of the material interests of transfems is never quite advanced. By some mechanism, by some unexplained (and sometimes metaphysical) force they benefit from "sex based oppression" in ways that e.g. an infertile cis woman would not. It essentially doesn't matter, it's an a priori assumption. "Belonging" to the "male sex class" itself is thought to grant access to structural power and the ability to benefit from "sex based oppression", even when no real world mechanism to that effect exists.
"Hating men" is neither a defining nor a unique feature of TERF ideology. There are some TERFs who arguably do hate men and there are others who do not. There are feminists who "hate men" in nearly every school of feminism. Even the most toothless iteration of liberal "girl power" feminism had its "male tears" mugs. The defining feature of TERF ideology is the exclusion of trans women from its conceptualization of women's oppression and from feminist organizing, justified with the supposed "class interests" of trans women being those of the "male sex class".
Trying the redefine the meaning of "TERF" in an attempt to obfuscate the specificity of this ideology's hostility towards transfems is dishonest and transmisogynistic on its own. Trying to do so while also claiming that transfems' material interests actually do align with those of cis men, the central distinguishing claim of TERF ideology, is such an unbelievably repulsive act of hypocrisy that it should disqualify anyone who does so from participating in the discourse surrounding trans women's oppression entirely.