The speaker wants to hate someone, and wants it badly. The phrase "with every fibre of my being" shows how much effort and intention is behind the wish. Hatred would be simpler: it would end the hurt, draw a clear line, and let the speaker move on. But the final line admits defeat. Love is still there, and it won't let hatred in.
The poem is only four lines long, and its structure mirrors the feeling. The first three lines build up determination, then the last one quietly undoes it. The word "impossible" is blunt, as if the speaker has tried and failed more than once. We don't learn who "him" is or what he did, and that gap makes the poem feel personal and unguarded. The mood is weary and tender, with a hint of frustration. The speaker seems hurt, but also stuck, caught between anger and affection and unable to choose either one cleanly.