Extrapolation is an essential tool for going beyond the known data. It allows us to project beyond the data and so fill in some blanks. But which blanks--and how validly? Extrapolation is based upon an assumption of consistency. That is, one assumes that the empty spaces will be much like the already filled spaces.
Now imagine that you can only see a small slice of the movie. Make the problem easy at first. Let's focus on the part where the penny is rolling steadily. Let's take only a slice of that. There's much we can know from that. It's definitely Abe Lincoln's image. And the mint date never changes.
If we extrapolated from that small slice of data we would be forced to picture a penny endless rolling. We could only assume that it would sooner or later wear down.
We would know nothing about the drop, or the bouncing (less and less) or the wibblewobbling preceding the final collapse. Those realities would not exist to us if we extrapolated from the small slice and assumed consistency throughout.
If we extrapolated a slice of the dropping we'd get endless dropping. If we focused on the penny laying still, at the end of its adventure, we would easily assume endless stasis. We would have to work very hard (and go out on many limbs) to assume any prior movement , let alone its varied moments and causes.
Now apply that to the current theory of where we are and how we got that way. The theory of plate tectonics, in essence, looks at the current micro-slow movement of plates and is compelled to assume, based on the prior assumption of consistency, that creeping has always been the case. Millimeters and centimeters of movement are extrapolated from. From that comes estimates that large continental plate movements have taken millions of years. And, most important, can ONLY have taken millions of years.
Sudden, cataclysmic events can no more be part of the picture than the drop of the penny or its final collapse are part of the extrapolation from that tiny slice of rolling data.