[American Constitutionalist]

" Why is the responsibility of the United States? "

I think it has something to do with a treaty we signed with South Korea, now, the question is ? will Obama honor that treaty ? or find some loophole to weasel his way out of this thing ? .... and the same goes with the treaty we signed with Taiwan to help protect them if China decided that it's time to make Taiwan a part of the Communist block of China...

[JimSEA]

Great answer. Might I add that we have troops in Korea in the
now forlorn hope of keeping China and Russia on the sidelines
in the event of just this sort of situation.