Cherry picking

Cherry picking, or "counting the hits and forgetting the misses," refers to the practice of choosing quotes and research which supports ones views while ignoring credible quotes and research, in the same branch of study, which undermines or contradicts ones views.

Examples
A Christian pacifist might quote the sermon on the mount:

while ignoring the Christian marines' favorite bible quote:

Christians opposed to gay rights often cite Leviticus to support their views:

while ignoring many laws in Leviticus and elsewhere in the Old Testament that condemn things like eating shellfish or require animal sacrifice ("But that's the Old Testament").