Again, I know that. But real people are not logic machines. They have limited attention spans and tend to latch on to criteria that they think feel right. Have you ever had to argue about why mylenation of neurons has no impact on personhood? I have. Why? Because a person heard that criteria, liked where it placed the line, and stuck with it. A lot of people want to set a line somewhere between the first and second trimester or somewhere in the second trimester (this is, in part, why "viability" is so popular). The pain criteria gives them such a criteria. While you and I both know that it isn't an exclusive choice, there are people who will latch onto it an use it as their only criteria.
If you think you can prevent abortions by using this argument with individual women, by all means do so. My wariness has to do primarily with the bigger debate.
The point you are making is that people are different. Those that grasp at one criteria they can live with are those that will not grasp those they cannot live with. You will not convince that person any further. At this point in history and on another subject, France and Iraq are such entities.