(As opposed to “no more oppressed, in different ways, than hypersexual people or people perceived to be hypersexual for whatever reason,” which I think is a fair argument.)
Let’s see: I TA’d a college-level Human Sexuality class in 2007 in which asexuality was not MENTIONED, let alone covered, a significant form of erasure mirroring numerous other erasures outside of academia.
…Which has been suggested as a major reason that bisexual people suffer higher degrees of depression and substance abuse than people who identify as gay or lesbian, in case you’re one of those people who think that erasure is not oppression. Another potential cause is general exclusion from straight and gay communities, which, oh look.
alierakieron mentioned the threat of corrective rape.
For aromantic people (as well as single people generally, but affecting people who don’t ever even want to marry more broadly), the ways in which marriage is used to assign rights and privileges in the United States is unfair and oppressive.
Family and social pressure to “meet the right person.”
Douchebags like Dan Savage saying that they “inflict themselves” on others, mirroring the sentiments of close others with less of a soapbox but probably more of an immediate effect on their lives.
As previously mentioned, asexual people are likely to be identified by others as queer and treated accordingly (perhaps particularly in secondary school settings?), and it doesn’t actually matter to their tormentors if they are “queer likes the same sex” or “queer we assume they do.” Sexuality and gender are entangled in our culture—I’m not a huge fan of Rich overall, but “compulsory heterosexuality” (or as Pascoe later described it in high school boys, “compulsive heterosexuality”) is a useful concept. Failure to perform, as well as “deviant performance,” is punished.
These are a few things that occur to me off the top of my head, as someone who is not asexual. So I’m sure there are plenty more.
Jesus wept. Not that I’m surprised, as a bisexual woman, that there are a lot of people who identify as queer who are deeply invested in keeping a lot of other people out. I’ve just been successfully avoiding them for awhile, I guess.