If each human who ever lived flipped 1000 coins a trillion times, it shouldn't happen.

If there were a trillion planets, each with a trillion people, each flipping 1000 coins a trillion times, it shouldn't happen. Not even close.

Yet, if you get 20 people in a room, there’s a near 50/50 chance that 2 folks have the same birthday. Equally mind blowing.

So yes, people are pretty bad at probability.

The naive (and incorrect) deduction that one might make is that you start with 1/365 chance, so by adding twenty people you make it 20/365 that is 5%. So instead of the estimate of 5% the correct results that account for all possible comparison ends up being 50% - an order of magnitude higher.

The difference is substantial but it is not on the same orders of magnitude that this problem or the other examples are.