Please go to move 157. Black just played the marked move and White can live eventually. Why didn't Black hane at P2 instead? For me that would have killed White's invasion and I see no other benefit for White there.

Because of the aji of the O7 cut ? If white has a stone around p3 in sente trying to live and then cuts, black's M2 stones do not have two eyes. I'm not entirely convinced by this explanation as it seems the m2 stones can cope but I don't see anything else...

And I guess black counted that letting white live did not put him behind in points.

8ds can make mistakes.