Age has everything to do with it.
Imagine if you had say, 5 pounds of cookie dough between your hands. In one scenario, you squeezed the cookie dough together very slowly. It squished and pieces of it had risen above and below other pieces. When you squeeze the dough slowly, youre building dough mountains just as plate tectonics slowly builds mountains.
Some young earthers believe that continents moved quickly during the flood, that Pangea was split by the oceans of the deep. Antarctica has tropical trees, fossilized beneath its iced sheets. Some propose that Antarctica moved from the equator to the south pole quickly, in response to this flood. Others propose that the flood built the mountains.
With cookie dough, if you smash your hands together at 50 miles per hour, the dough would become obliterated and would fly all over the walls due to the high amounts of energy transferred from your hands to the dough. This analogy is more in line with young earth views of accelerated continental drift. And so to would continents, mountains even, be obliterated in such a high energy environment where in a matter of days, continents were pushed apart hundreds of miles.
Time, lots of time, millions of years, makes the most complex geologic features, much easier to explain as they can be built one step at a time, without the need of super high energy, physics defying, rationality defying occurrences.
But, beyond that, its just more reasonable to recognize these events (mountain building and continental drift) as slow events, because this is as we see them in todays world, theyre very slow, and we know it works, its possible and it is what is happening now. The continents move very slowly (about the rate our finger nails grow, this is observed today). And so, it would take many millions of years for them to separate (African separating from south America for example).
And would you believe further that rates of tectonic drift also correlate with radioactive dating of the hawaiin islands? Two completely independent observations from different fields of science. Synchronized. A coincidence? No. It isn't a coincidence.
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