I have nothing against him personally; I just think there's a better candidate.

have 在这里是助动词，与 nothing 搭配构成否定表达，表示"没有"。 against 是介词，本义是"反对、对抗"，在这里引申为"对...有意见/不满"。 have nothing against 是一个固定短语，意思是"对...没有意见/不满"。