Why do rhythm and rhyme sound so pleasing to the human ear?

Answer 1

because of tradition. before the writen word (or before most people could use it rather) rythem and rhyme were the only way people remebered things. for example: "green sky at night, farmers delight; green sky at morning, farmer take warning".

Answer 2

Here is the great secret about poems and sound. A great poem is hard to read aloud because it takes your breath away. This is a good problem.
If by its sounds the poem has rendered you speechless and if the sounds come to mean something important to you in that moment
then- -no matter what rules ought to apply, the poem has done it job.