Pseudoexoagrophobophilia.

Misperceiving others to be aggressively phobic for pleasure or gain.

The hate one wishes one could display through the projection of an Other.

The Golden Rule, Inverted: Hating one's neighbor as one hates oneself.

When the one who hates themselves (the first person) is in denial about their own self-hate, the only way that they can project this denial onto another while still relating to them is to be in denial about how the second person must be in denial of their lack of hatred of a third person. The first denial is their own hate of themselves, the second denial is inverted: they are in denial of the second person not hating the third person. The third denial is that the first person secretly hates the third person, but since the first person can relate their own secret self-hate with their secret hate of the third person, this dual-denial seems to invert and then revert the hatred of who they hate into a form of contorted love or camaraderie.

Person 1 hates person 1 / claims to love person 1 => denial #1

Person 1 loves* person 2 / claims to hate person 2 (for hating person 3) => denial #2

Person 1 hates person 3 / claims to love person 3 (through hate-relation) => denial #3

*(finds utility in)

The person in the middle (the second person, the projected upon) is the open scapegoat by which both the secret hater (the first person, in denial of self-hate) and the secretly hated (third person, actually hated by the first) are aligned against, whether they are aware of it or not.

A cheap, yet probable, example (see 2016 suburban voting): a white 'woke' woman is seen decrying a republican man of being racist (even though he might not be, but is easily portrayed to be) because she is afraid of a black family who lives down her street. She knows that she can't be implicated as a racist and still retain her social status (and maintain her self/other hatred without being found out), so she uses the republican man as her situational 'sword & shield' by proxy against the black family (and to buff her own self-esteem through the comparison of herself to the newly minted scapegoat).

The deviousness of this situation is that only the second person and the third person actually get dealt any real social/physical/emotional damage. There must be some sort of self awareness within the first person that knows that they can profit from this arrangement seemingly perpetually. This is probably why they hate themselves, honestly: unexamined, unmitigated guilt.

Now extend this to group identities and you have The Problem enumerated.