Nobody is denying that extrapolation is legitimate in science. But the devil is in the details, and not all extrapolations are equal. Some extrapolations can be unwarranted.
We just recently here had yet another of our repeated debates about microevolutionary vs. macroevolutionary change. I’m not going to continue that debate, even if the usual suspects try to bait me, but will refer to it here only to make a point about extrapolation.
If, as many here believe, macroevolutionary change is caused by nothing but repeated rounds of microevolutionary change, then it should be possible (in principle, anyway) to extrapolate back from present-day forms to ancient, very simple forms, imagining a series of steps working by mechanisms we are familiar with. But if, as some evolutionary theorists have suggested (and again, I won’t be baited if some here repeat their claim that no evolutionary theorists hold this view), macroevolutionary change requires more than the type of changes we see in microevolution, then it would be unwarranted to reason back, imagining a whole chain of events entirely like those which lengthen the beaks of Galapagos finches, to the most primitive life forms.
Note that I am not here challenging common descent (which is not surprising, since I’m not a creationist), but talking only about evolutionary mechanism. Granted that the transition from one-celled life to man happened somehow, one cannot assume that it happened solely by additive rounds of microevolutionary change. There might be other things going on.
To take a really crude example, I might observe you walking X miles per hour, and calculate that you can walk X miles per day, and from that, calculate how long it would take you to get from any point to any other point on a globe 25,000 miles in diameter. So, if I find out from a friend (who saw you at the Louvre), that you were in Paris a year ago, and I extrapolate, based on your walking speed, to produce a history in which you walked from Paris to Cleveland, is the extrapolation justified? No, it is isn’t, because you can’t walk across the Atlantic Ocean. (Unless you’re Jesus, of course.) A mechanism other than walking would be necessary to get you from Paris to Cleveland. I can be sure that you got from Paris to Cleveland (since you’re in Cleveland, and you were in Paris), but I don’t know how you got there, not even if I know every conceivable detail about the physics of walking, the length of your legs, the strength of your leg muscles, etc. “Travel from Paris to Cleveland is just travel from Paris to Le Havre carried out over a longer period of time” is an unwarranted extrapolation.
Of course, I think you are attacking the position of people who, unlike me, deny common descent itself, but the point I’m trying to make here is not that all creationist objections to evolution are reasonable (they aren’t), but that it isn’t entirely wrong to question simple extrapolations, where simple extrapolations are suspect. Forensic scientists can tell you, in some cases, that a bullet was fired from such-and-such a height, based on the angle a bullet entered a body, etc., because extrapolation backwards to the source of projectile motion is a comparatively straightforward matter. But if evolution is a multi-level process, with causes at one level being different from causes at another level, analogies from ballistics or other sciences, focusing only on the lower-level tier of evolutionary causes, will be misleading. And some of the people who have made this point are atheist or agnostic scientists who are far from being creationists.