Don Marquis' argument about the immorality of abortion is the most successful philosophical argument that I have ever seen. He takes a slightly different approach:
0. The presupposition is that it's wrong to kill a normal adult human being. If we cannot agree on this then we cannot proceed with this discussion (or any discussion).
1. The reason it's wrong to kill a normal adult human being is that killing them harms them. It harms them by robbing them of future experiences -- specifically future human experiences (which are seen as intrinsically valuable).
2. When a fetus is aborted it is also being robbed of future human experiences.
3. Therefore, if it's wrong to kill a normal adult human being, it's also wrong to abort a fetus under the usual conditions of abortion.*
*not considering cases of rape or if the fetus threatens the life of the mother. These situations are not the norm and are obviously different, so they should be evaluated separately.
The problem is that this argument can be extended beyond conception, namely
1. Harm is the denial of future experiences.
2. When you stop a rape, you are denying the sperm of the rapist from having future experiences.
3. Therefore it is wrong to stop a rape in progress.
Or if you don't like the idea of rape...
1. Harm is the denial of future experiences.
2. When you discourage your daughter from having sex at an early age you are decreasing the chances that her eggs will have future experiences before being flushed out.
3. Therefore is is wrong to discourage your daughter from having sex at an easy age.
The crux of this is that it puts value on potential future experiences without caring at what state the existence is at now. I thus propose an alteration:
1. Harm is the denial of future experiences/memories to an entity that already has experiences/memories. (Thus murder is bad as it denies future experiences to an adult human, an entity with existing experiences)
2. Fetus's from 20ish weeks after conception and forward have memories/experiences
3. Thus it is wrong to abort fetus's past the 20ish week mark.
This gives us a decent framework while at the same time stops silly logical conclusions such as protecting sperm.