shematwater:

You can remove the child at three months and have it survive. It is not common, but it can be done. Anyway, this does not make it any less of a child, not to me. With this idea you have to say that the elderly people who can no longer care for themselves are no longer people. It seems to be the same argument.

Two items that I feel need addressing. First, where do you get information that a fetus at three months can survive? Because the sources I find on the subject don't agree. The news item they reference is about a year old, but I am skeptical that the medical technology has advanced that far in a year. Could be possible, but I wouldn't mind seeing a reference. From wikipedia:

The earliest gestational age at which the infant has at least a 50% chance of survival is referred to as the limit of viability. As NICU care has improved over the last 40 years, viability has reduced to approximately 24 weeks,[27][28] although rare survivors have been documented as early as 21 weeks.[6]

As for your other premise, equating the fetus with an elderly person, I dispute your claim that it's the same thing. Your point of comparison apparently refers to the need for care, being helpless? In that case, you could point to infants or even young children as well, clearly an argument the pro-choice crowd does not make. It seems reasonable to suspect that the pro-choice argument is not based on a fetus' inability to care for itself.

Moreover, elderly people do have characteristics of life that a fetus at early stages does not -- brain activity, for example, sufficient to respond to the environment -- which a fetus does not develop for some time. (source here) So there are other possible criteria we can use.