It's because genes are highly conserved, and I should have been more precise: we share about 50% of our genetic code with bananas. Intuitively this makes sense, since genes code for proteins and we can eat bananas (which can in turn eat us, with some help).
If you count the exome, which is not highly conserved because it doesn't play much of a role that we know of other than coiling, it's more like 1%. So "50% of our DNA" is not accurate, it's our genes.
Granted the persistence of humans provides quite a bit more, and implies the survival of (some) culture as well, which might matter more.