Actually the abortion argument today has very little to do with the question of when life begins (almost all parties who look into it agree it is conception). There is some disagreement about the end of conception, whether it is fertilization or implantation or the point after which twinning is impossible. That is a narrow range and has little impact on the abortion debate except the morning after pill.
As 92 noted, some argue being a human is not the same as being a person. A person is defined as a being capable of some higher mental function like self consciousness or the ability to reason. They argue abortion is killing but not killing a person. more like killing a fish. The problem with these arguments is that it also allows infanticide, since infants do not function higher than a pig, and we kill pigs.
The other main argumen, the one that is literally "prochoice" ( and directly influenced the primary opinion in Roe v Wade,) is the so called libertarian argument that the woman is simply not obligated to the fetal person any more than she would be to any other separate person, for example a beggar. it would be awfully nice of her to assist, but it is charity not obligation. The fetal person has rights but only the same rights as anyone else. As I do not have the right to demand that you feed me, neither does the fetus. It is a mere accident that it dies. The argument suggests there is a right not to help, but not a right to kill. Therefore after viability, aka the second trimester, abortion is direct killing and no longer a neutral act. Hence the Roe v. Wade second trimester restriction.
When people say life begins at conception and therefore abortion is wrong, they are usually taking it for granted that every human is by nature a person (a rational and self conscious being, or the bearer of moral capacities) but in an unexpressed or incipient state. They are also usually assuming the woman is for one reason or another responsible for the welfare of the fetal stage human. If these two points were established instead of assumed, the pro-life argument would be extremely strong.