For some people, it is literally a fear that they ways in which they are specially privileged is being attacked. This was particularly obvious in the debates about equal marriage in the noughties and tens; people claiming that same-sex marriage would 'devalue' their own marriage. Which, in their eyes I suppose it might, because it would diminish how special they were.
But you see similar themes in most anti-equality movements, just generally a bit more veiled (I was kind of astonished how _blatant_ the opponents of equal marriage were about basically admitting "we object to this because it is an attack on how society considers us to be better than you").
But you see similar themes in most anti-equality movements, just generally a bit more veiled (I was kind of astonished how _blatant_ the opponents of equal marriage were about basically admitting "we object to this because it is an attack on how society considers us to be better than you").