It's a fairly common notion to "sweat out" a flu. Stay in bed, wrap yourself up in lots of blankets and just sweat the damn thing out. High body heat kills the virus.

So it would make sense that drugs like tylenol/paracetamol would make you feel better, but would keep the flu alive in you for longer.

Anecdotally, I have used this technique many times, also drinking hot tea besides being wrapped in blankets, and at least for me it has worked much better than when taking any kind of antipyretics.

There are cases when the fever is dangerously high and antipyretics are necessary. But when the fever is supportable it certainly accelerates the healing.