I didn't get the impression that she was quite at that stereotype "incel" place. Not quite that bitter, despite the headline. Reading this, I felt that she was in transition of ideas... possibly some disillusionment. Maybe shedding some ideas that no longer work for her.
I think there are two defining aspect to that "bitterness place" we associate with "incel philosophy."
One is intense philosophical rationalising of negative feelings. Hence incel "theories" with Chads, Statcies... latching on to OKcupid blogs and the typically bitter spins on sex statistics. It tends to resolve to very nihilistic worldviews. Incels are really just one famous subset of internet bitterness philosophies. There are many, and they often drift to recurring "bad old ideas."
I think that's the vibe you're picking up. The author is clearly philosophically oriented, and navigating her experiences this way. Since she seems to be in a bad place emotionally, her takes on philosophy have this ring.
The second aspect is a, partly imagined, negative "conversation" with society. Feel rejected by women, hate women, hated by women, rejected by society, reject society... People don't enjoy bitter company, and lack of company is embittering. Mutual shunning and conflict, most of it in one head.
I don't get this part at all. She's not rejecting society back, but is feeling somewhat rejected. She also seems quite self aware. "Try to channel my emotions into better philosophy," implies that previous philosophy wasn't.
Personally, I think people mistake what philosophy is. It's not usually a pursuit of truth. There is no "truth" about the worth of a person, society or whatnot. Philosophy (the ones she's engaging in) is about rhetorical frames, perspectives, ways of thinking. It's art. Philosophies are relevant sometimes sense, but rarely "true."
Peter Singers' utilitarianism (I suspect he's her main culprit) is dehumanising to everyone, if you think of it as applying personally to you. Earlier iterations (eg Bentham) have even resulted in nightmarishly dehumanising prison systems, factories and such. OTOH, it's also very affirming of altruism and has had positive result in this regard.
The way people feel about Singer tends to be closely related to their emotional state. One essay can be a call for some awful eugenicist nightmare or benevolent mutual love... depending on the readers' mindset and which threads they stretch to their "logical" conclusions.