Why was East Pakistan even part of Pakistan in the first place?
It was Muslim majority. The basic idea was that Muslim majority areas went to Pakistan, other areas went to India. Since Muslims were not neatly distributed this meant that Pakistan was composed of two separate areas, both of which had (and still have) Muslim majority populations.
This question was answered in another thread a couple of days ago: http://www.reddit.com/r/explainlikeimfive/comments/24m8c2/eli5_why_is_the_bengal_delta_not_part_of_india/