Because it doesn't make any sense, and can lead to contradictions.
If I have 2*0 = 1*0, this statment is true, but I can't divide both sides by 0 to get 2 = 1. That's false.
100 divided by 4 means "If I have 100 objects, and wanted to make sets of 4, how many sets would I have". The answer is 25, because 25*4 = 100. If I had 100 objects and wanted to make piles of zero, how could I do that? If I handed you "nothing" over and over again, I'd still have 100 objects left over to divide. If 100 divided by 0 was some number, say x, then 100/0 = x. But this would mean 100 = 0*x. You can't mulitply a number by 0 and get 100 back.
Dividing by a number very close to zero gives you an astronomically huge number. You know that dividing a number by a fraction, say a/b, is the same as multiplying by b/a. So x divided by 1/10 is x * 10 = 10x. And x divided by 1/100 is 100x. And x divided by 1 / 100,000 is 100,000x. So as you divide by numbers closer and closer to zero, the result gets bigger and bigger.
BS & MS in mathematics