1. polarize

If something polarizes people or if something polarizes two separate groups are forms with opposite opinions or positions.

e.g. Missile deployment did much to further polarize opinion in Britan.

2. dilemma

A dilemma is a difficult situation in which you have to choose between two or more alternatives.

e.g. This is the crux of the present dilemma.

3. crux

The crux of a problem or argument is the most important or difficult part of it which affects everything else.

e.g. He gets though the crux passway between technology and commerce.