It's not that it's a major no-no. There are two main reasons for choosing not to eat aspartame: 1) for some people it stalls weight loss 2) aspartame has been found to cause cancer. Also, during induction you're trying to wean yourself off of sweets. If you're drinking diet sodas a lot you might be more tempted to maybe cheat. Plus, aspartame is a chemical, and do you really want to be consuming tons of chemicals?