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She probably won't accept what I have to say.
Literal
She [topic-は] my point [object-を] accept-and [for-me-てくれる] won't probably [resignation-な].
言い分 means 'one's say / one's point / one's claim' — the position someone wants the world to acknowledge, often with a faint defensive or grievance-laden flavor (like English 'one's side of the story'). Three layered grammar points compress into the second half: 認めて (acknowledge / accept, te-form) + は (contrastive topicizer adding 'as for accepting...') + くれない (negative benefactive 'won't do for me'). The clause-final だろうな combines the inferential だろう ('probably') with な (resignation/sentiment particle), giving the whole sentence a tone of weary acceptance: 'no, she won't.' The contrastive は here heightens the sense of 'she might do other things, but accepting my point — that, no.'