In Pitch Perfect, Jesse says to Beca:
I don't get where he's making this generalisation from. Yeah, she was a prat to Jesse himself, but I can't think of how else she pushes people away.
Firstly, Beca wanted to go to Los Angeles and become a music producer but her father refuses it and forces her to become a student at Barden University in Georgia. If you've observed Beca's character keenly, in the beginning she's a recluse and doesn't want to make any friends. On the other hand, Jesse likes Beca and wants to make her a socially acceptable person.
I remember, in one scene, due to some misunderstanding, Beca is taken to the local police department, at which point Jesse and Beca's father bail her out. Angry at Jesse for calling her father, she tells him to "back off," since "you're not my boyfriend." Jesse is visibly hurt by her words.
So, Jesse cares for her but Beca keeps disliking him. When Jesse said "You push away anyone who could possibly care about you, Why is that?", I think Jesse is referring himself while saying that line because he's hurt by her even though he's trying to be nice with her.
This is an overdramatized and irrational generalization that is often made by persons who assume that they have a right to be in someone's life when that person interests them.
There is no justification for what he says, and in the context of our society's history this could be seen as a male-/ego-centric trope of the asserted assumption of the necessity of women to be interested in the men making attempts to be in their lives.
Past experiences do not afford, require, or presuppose future experiences, and as a person, we -- all persons -- have the right to make choices and live however we want, with or without whoever we want, at any and all moments.
That is the crux of the notions of consent and self-worth.
This statement was a selfish, narcissistic act of guilt-baiting. It was an attempt to marginalize her self-worth by mansplaining that she was being selfish and self-destructive by not being with him when he was making attempts to be with her.
Whether or not her choices were the most healthy or respectful, to herself or others, there is no presupposition (ever) that a person is required to be in, or be open to, another's life.
She may have been overwhelmed, dramatic, upset, and confused, and she did lash out in anxiety and anger. While those are not great things, they were the reality of her circumstance, and they were mistakes that she needed to understand and move forward from. They are not exemplars of her inability to meet some fantasy normalization of appropriate being. And they should not be met with the denigration of her circumstances under the presupposed assertion that her life is going poorly because he is not in it in the way(s) he wants to be.
This approaches the kind of subversive normalizations that undermine the intelligence and sanity of persons based on the arbitrary particulars of their birth and natural existence (like accusations of being "hysterical"* due to one's uterus and menses.).
While he is sad and hurt that she was rude and angry, and he does wish to be in her life, and we should probably assume for generally (mutually) good reasons, his response is not indicative of true care, love, and kindness. It is a selfish response that simultaneously self-aggrandizes while mitigating her current circumstances.
It is a trope-y response to hetero-patri-normative societal expectations of he-said-she-said romance, creating unnecessary drama that will be immediately overcome and forgotten, as if the final state of their relationship is made stronger by arbitrarily irrational previous "difficulties".
Relationships are continued manifestations of choice, trust, love, and care. Patience and respect are the natural responses, and characterizations that do not healthily and rationally portray the appropriate responses should not be seen or normalized as appropriate, rational, or healthy.
There is no reasonable explanation for his statement and facetious question, except as his own act of disrespect.
*Note that "hysteria" derives from the Greek root hystero- for "womb", as seen in "hysterectomy", the surgical removal of (part of) the uterus.