We like things that have one and only one answer. Dividing by zero can generate more than one answer.
Take 10x/5x. For all non zero x the answer is 2. So it sure looks like it should be 2 at zero.
Now take 4x/4x. For all non zero x the answer is 1. So it sure looks like it should be 1 at zero.
In fact, you can get all kinds of answers that look right. This ambiguity leads us to say that it cannot be done, as it is ill-defined.
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