In the absence of feats of strength or other measurable exploits, males in social drinking situations will often use bladder capacity as a gauge of masculinity. Excuse yourself to piss early and often, and you’re apt to find yourself subjected to good-natured ridicule. Apparently that’s what’s happening here. Lucky Eddie has to pee. Hilarious. He may want to look into Oxybutynin.
As an aside, take a good look at Hagar’s expression in panel one. I saw many examples of that general demeanor during a recent visit to Green Bay. Not a lot of happy people in the bars there, I tell ya.