。
She wouldn't tell me why she had gone home ahead.
Literal
She [topic-は] why first home [to-に] returned [question-か] me [to-に] try-to-say didn't.
An embedded wh-question inside a refusal-to-speak frame: なぜ先に家に帰ったか ('why she went home first') becomes a noun-phrase argument of 私に言おうとしなかった ('didn't try to tell me'). 言おうとしなかった is the negative of 言おうとする ('try to say'), built on the volitional 言おう + として — capturing not just that she didn't tell, but that she actively wouldn't. 先に ('first, ahead') here means 'before others / ahead of schedule.' The whole sentence carries an emotionally loaded undertone of suspicion or hurt feelings.