Fletcher Christian: And why the heck should the West in general, and America specifically, help people who hate us?

Because it is the moral imperative of the religious tradition which underpins the West, that coincidentally is referred to by the same sounds you make when you say your last name.

Matthew 5:

[44] But I say unto you, Love your enemies, bless them that curse you, do good to them that hate you, and pray for them which despitefully use you, and persecute you;