[url=http://en.wikipedia.org/wiki/Human_brain_development_timeline]Actually no, the brain doesn't spring into existence at the moment of birth.[/url]
To answer your main question: because they believe you are killing a person. Whether or not you agree with them, you should recognize that's not an unreasonable motivator.
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Edited by RighteousTyrant: 1/28/2013 9:16:25 PMSeconding this post because Baha is correct, especially on the bit about failing to recognize the motives of the other side (or failing to recognize that they're motives aren't unreasonable). Politics in general could use some more of this understanding mentality.