I have always been perplexed by this. I could come up with a faux scientific explanation, but I'm not in the mood.
Interestingly, the stinkier underarm has changed over time. By my estimation, every 6 years one armpit takes over the stink superiority or inferiority if you like.
Strangely, the opposing armpit has almost no smell whatsoever---although this could be desensitization as I never remember to smell the less offensive armpit first. Thus, I am always experiencing sensory overload as I go to check out the relative stench of my allegedly unoffensive underarm.
Any thoughts? By the way, I am currently (for the past 3 years or so) dealing with a stinky right armpit and a neutral smelling left armpit.
Truthfully, I don't even use deodorant on my left side some days---it is that little of an olfactory concern.