The first reason is dice simplification. What I mean by that is that for some reason, % dice scare people but regular numbered dice do not. So if you can reduce everything to 5% brackets an easy simplification is to use a d20. Using the even/odd method with d20 does work, but you get a fairer distribution with the 50% method. This is a very minor reason to use the 50% method but I thought I'd mention it.
The primary reason I would recommend it is because of flexibility. Some tasks may be easy to perform but hard to truly get outstanding success at, so you may want to make them 30/70 distributions. Or the chance of a major failure may be much greater than major success, giving a 50% on success but 70% on failure. It also leaves open the opportunity for other things to influence the degree of success (DoS) that don't affect the base chance of success. IE a legendary science officer may have an ability that grants +10 to DoS for sensor checks, while an officer with an unreliability penalty may affect failure DoS for diplomacy by +5
Mostly I personally don't like the even/odd mechanic, so I admit bias, but that doesn't mean the 50% method is wrong either.

--Mav