。。
It looks like she'll refuse his advice — because she doesn't like him.
Literal
She [topic-は] his [genitive-の] advice [object-を] looks-likely-to-refuse. that-is-because she [topic-は] him [subject-が] is-not-liking [because-からだ].
A two-clause discourse pattern with なぜなら~からだ ('the reason being that...'): the first clause states the prediction (she'll refuse), the second appended clause provides the cause (because she dislikes him). なぜなら is the explicit, somewhat formal way to introduce a justification — common in writing, debates, and explanatory speech. The closing からだ ('it is because') seals the explanation and is required for the なぜなら frame to feel complete. ~そう attached to the verb stem (拒みそう) gives the appearance/inference reading: 'looks likely to refuse.'