Well, no, I think the OP is making a point about the magnitude of the risk. Alcohol is clearly far riskier than chewing gum. (I say this as someone who drinks alcohol and chews gum, though not at the same time.)
If you are going to bring numbers into it, then bring numbers into it. What are the cancer risks of alcohol? How does it correlate with the number of drinks per day or week? How does cancer risk correlate with aspartame? What is the ratio of risk from daily chewing of aspartame gum vs a glass of wine? If you don't know, then your argument means nothing.
And even then I'm only speaking of overall risk. They are additive, not zero sum. If you eat aspartame and drink alcohol your risk is higher than doing either one by itself, no matter what the numbers are.
The cancer risk from aspartame seems to almost certainly be 0. The cancer risk from alcohol is known to be higher 0. Avoiding aspartame for cancer-related reasons while drinking alcohol is non-sensical.
