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I know that this question has been asked, but I cannot understand what the hell they are talking about. Can anyone just straight up give me the algorithms?

With the M or M' move you basically move 4 pieces let say 1 2 3 4 in the order 2 3 4 1 because you can get from 1 2 3 4 with 2 pair swaps like swap 1 2 than 2 3 and than 3 4 , we used 3 pair swaps , that makes it an odd parity

It follow the same principles as numbers so a odd and odd parity is even and an odd and a even remains odd

How is destroying all four F2L pairs better than destroying just two cross edges which are trivial/fast to repair and even keeps corners oriented (and permuted)?