Why would I ever choose rolling hit points?

In DnD 5th edition, all classes seemingly have the option of rolling hit points -or- just increasing their hit points by a set value.

That set value is defined as the dice roll’s average, rounded up.

Given that it is rounded up (and thus will statistically offer better HP than rolling), why would anyone ever roll for hit points? Rolling seems to provide the worst of both worlds, giving you lower HP than defaulting as well as possibly screwing your barbarian over with a roll of 1, and just risking plain bad rolls in general.

It makes me wonder if I’ve overlooked any rules that otherwise balances the options. Am I?

Update: From some of the answers given below, I sense an answer along the lines of “it’s a roleplaying game, so there”, which to me is an unsatisfactory answer due to all other roleplaying games I know of (outside the D&D/Pathfinder line, of course) relying on deterministic methods.