We want to formulate the laws of algebra so that
if a = bc, then a/b = c
provided that a/b is defined at all. If we defined 0/0 to be 1, then
0 = (0 times 42) (for instance)
would be true, but
0/0 = 42
would be false! It seems less confusing and dangerous just to forbid division by 0 absolutely, so that equations of the form 0/0 = c never need to be considered.