If you look it up, a common-sense definition of a slur is simply an insulting remark, that might also harm someone’s reputation. This is over-simplistic, in that it doesn’t consider power dynamics. Often when we talk of slurs we’re talking about language used by those with power (which can mean being socially normalised, not demographically vulnerable to systemic forms of discrimination) to bash those without, in a hateful way associated with some kind of disenfranchised group. I would say minority group, though importantly women of course experience all kinds of misogynistic language despite the size of the demographic (spoiler: because patriarchy). Most people can recognise and be suitably disgusted by a wide range of slurs, particularly racial ones. There’s also the conversations constantly happening within marginalised groups around the politics of reclaiming previously weaponised words as a form of empowerment – slutwalks, self-defining fags and dykes, and the now quite longstanding world of queer. But due to the (sometimes faltering, and certainly incomplete) progress that has been made through decades of social processes whereby more and more people get switched on to how language is used being something that matters, legitimate processes of challenging oppressive language have been levied as a rhetorical shield against being criticised, or even described.
I would argue there are two particular terms in relation to transgender people in particular that ignorant or prejudiced individuals like to claim are slurs or pejorative – cisgender, and TERF. Cisgender, or cis for short, comes from the latin meaning ‘on this side’ (whilst ‘trans’ means ‘on the other side’). It is a value-neutral descriptor for individuals whose gender identities align with how their gender was assigned at birth. TERF stands for trans-exclusionary radical feminism, and describes people (usually women) who profess a feminist identity but do not consider transgender women to be ‘real’ women.
Cisgender exists in order to de-position the words ‘man’ and ‘woman’ as always being about people who are not trans (notice how trans men and trans women are always indicated by the prefix, but most of the time cis men and cis women are ‘just’ men and women?). When we say man, or woman, we don’t have any information about whether an individual is cis or trans, but for as long as cisness is positioned as the ‘default’, trans status is positioned as ‘not normal’, rather than minority. Transness is implicitly excluded from being ‘real’ men or women for as long as those words on their own don’t include a universal appreciation of the possibility and reality of transness. This isn’t to say that cis people can’t and don’t experience tensions, discrimination, or negative feelings because of enforced gender roles. But they do benefit from being viewed as real, constant, stable, and never having to convince or confess to others what their gender is, because it’s taken at face value. Cis people broadly benefit from being ‘the default’, and from cultural practices of ascribing gender to people based on what we see, and this often being taken as ‘more real’ than what an individual has to say about themselves.
People who don’t like these words existing often try to claim that they’re slurs in order to delegitimise their usage. Because of the fact that oppressed individuals may sometimes, in understandable frustration at experiences of inequality express their anger through disparaging the oppressive groups. Compare TERF to say, racist, or homophobe. These are words that are used to describe people with a particular set of (discriminatory) beliefs, or who engage in discriminatory practices. In those cases, people called homophobes and racists tend to respond by going ‘no I’m not! (I have a friend who is gay!)’ – yet fascinatingly TERFs don’t say that they don’t think that trans women aren’t women, but that… it’s offensive to say they are? In more extremely hateful individuals one does see people defiantly, proudly proclaiming themselves as racist, homophobic, transphobic – because they believe it is right to be so. Those who don’t believe it is right to be so but don’t recognise the problems with their actions are now the bigger problem.
People can try to shut down descriptors which shake their ignorant worldviews. TERFs see themselves as ‘feminists’, men and women critical of ‘cis’ see themselves as ‘just men and women’ (I’ve never seen a trans person have a problem or make a critique of the word cisgender, which probably has a lot to do with experiences of having their genders systematically delegitimised).
It is a Machiavellian, political move to utilise narratives of oppression resistance in order to reject descriptive labels that function to make a minority less Othered (in the case of cis) or to describe a set of beliefs unambiguously, making it easier to see their failings (such as TERF). One can see it in other domains – take the descriptor of ‘Blairite’ – because support for the political ideology of Tony Blair has been criticised heavily, proponents try to silence their critics through tone policing and claiming those labeling them are being offensive.
The bottom line – it’s important not to confuse people being pissed off with a group of people described by a word, and the word itself having a disparaging meaning.