Since atheists don't believe there is some supernatural entity dictating right and wrong, we have to employ reason to come to the fairest perspective we can. 

In the case of abortion, we weigh all the facts and find we must come to the conclusion that, on balance, there are some instances in which a woman's right to her own body outweighs the right of a possible person to be born. It's not an easy decision to come to but it is a rational one. Basically it comes down to the idea that a possible person is not as important as an existing person. Part of the reasoning behind this is that many possible people are miscarried by natural causes anyway. If we're to consider every possible person as being as important and cherished as every actual person we would have to live in a state of constant mourning at the cruel carnage being wrought (by God, presumably). 

Atheism isn't so much a belief as it is a refusal to conduct oneself according to superstition. We feel obliged to use our brains.