だいたい here is the rhetorical 'why in the world / basically why' opener for a complaint. パシる is casual/slang for 'to run errands (for a superior, usually against one's will)' — a verbalization of a school/yakuza-derived slang. パシらされる is its causative-passive: 'be made to run errands.' なきゃなんない is the spoken contraction of なくてはならない 'must.' のだか is a rhetorical-question nominalizer.