here’s how it makes sense to me:

What question are we actually asking when we ask “what is 8 divided by 2”? We’re asking “If I have 8 jellybeans and break then into two groups, how many jellybeans are in each group?” So Consider the question for 8/0: “If I have 8 jellybeans and break them into zero groups, how many jellybeans are in each group?” The question itself is invalid. Answering with any number wouldn’t make sense, the only response that would make sense would be “what do you mean? There are no groups!” It’s almost like it stops being a math problem at all, hence no mathematical answer.