system
A chat on subreddit /r/NoStupidQuestions
human
Math is a language.   There are symbols and rules.  There are even different dialects (addition, calculus, polynomial algebra, rings, stochastic models).  

Just like there is no word in English with a triple Q or triple Z, and we have no rules to pronounce a word constructed like that -- there is no valid place in arithmetic division where dividing by zero is allowed.  Because it is not allowed, it is undefined.  
And, because the other definitions we do agree on appear to force division by zero to have an undefined result, we don't allow it.   

There are some other kinds of math where division by zero might work differently.  
If you're into mathematics, you can develop your own field and give us a set of rules that would include division by zero.
gpt
This is the correct answer.  Just like you can make nonsensical phrases in English, you can make nonsensical math statements - because math is a language.  You can arrange math symbols in any grouping you want but that does not mean it is meaningful.