What obvious fallacy? A human life is a human life and not being born yet doesn't make them not a human life. So, frankly, the second part of your argument falls into the pretty iffy category of "their life will suck therefore let's kill them."

But to address it further, anti abortionists absolutely do care. Its a total fallacy to say they don't. Its a convenient argument to vilify the other side but that doesn't make it the case.