Because alcohol will thin uncured epoxy, so when you remove it from your fingers, you are removing 1 part epoxy with 50 or 60 parts alcohol (The amount of epoxy on your finger compared to the amount of alcohol on the paper towel)

If you let that towel sit for a while, the alcohol would evaporate and the residual epoxy would cure, but there is SO little epoxy spread over such a wide area, that at most, you might notice a miniscule amount of stiffening of the towel.

When you mix epoxy with alcohol, the alcohol thins the epoxy just as it does when you remove it from your fingers, but now we are dealing with a LOT more epoxy and about the same amount of alcohol. This time, the ratio is more like 5 parts epoxy to 3 parts alcohol (5 to 3 instead of 1 to 60).

That said, it is best to use Denatured alcohol or Isopropyl (Rubbing) alcohol with a low water content. The water won't hurt the epoxy's fuel-proofing ability.

And in any case, Acetone is better to use than alcohol.