I think the letter was a little bit childish

A relationship is something between two persons. Someone else (or many others in LZ's term) who "loves you to death" (such a chinese imprinted expression!) won't change his attitude or effort towards you. On the contrary, it would only irratate him.
Between you two, moody is one thing, bipolar is completely another matter. If he is true bipolar, maybe you should indeed run away. But if he is only moody, impolite, inattentive, then maybe you (both) should make more effort before giving up.