One thing that you'll notice soon after you run out of some of life's "necessities" when you come to Japan and need to go shopping is that there are very few brands of underarm deodorant in Japan. What little there is is under-sized and over-priced. The most common brand I encounter is "8x4". This is actually a German brand which is marketed in Japan and their PR states that it "leads the market" in Japan. Well, it's easy to lead the market when you've got no appreciable competition!
The reason there is so little deodorant sold in Japan is that most Japanese and Japanophile haku-jin (that's white people who believe Japanese culture and people are better than western culture and people on the whole) believe Japanese people do not stink when they sweat. The main explanation for this is that their basic diet is different. I'm not certain that this isn't true but there is really no proof one way or another.
The one thing I am certain of is that (this week alone) I passed no fewer than two Japanese people on bikes who stunk so badly of body odor that their smell powerfully wafted to me from 20 feet away. I'm pretty sure these particular parties could have used some "8x4". I'd have even purchased a can or two for them if I thought they'd accept it. There was also a tech support fellow at my former office who seemed to reek of sweat-induced body odor every single time he came by the office to fix things up. While I guess it's possible that most Japanese people aren't in need of a little unguent under the arms, clearly, some of them are. The general notion that they don't need deodorant keeps them stinking up the area rather than doing something about it.
I will note, incidentally, that it's not only Japanese people who don't require underarm deodorant. The fact is that my husband has never used it and does not smell in the least though he sweats a fair amount. This happens despite the fact that his diet is incredibly westernized. My husband's situation does leave me wondering if there are just as many western folks whose body chemistry is such that they don't need to swab their pits on a daily basis but the absolute terror at the prospect of offending others with our bodily odors is such that we apply deodorant prophylactically never knowing if we actually require it.
On a related note, there is an issue with the other side of this coin which is equally, if not sometimes more, offensive. This is the women who feel that perfume must be applied sufficiently lavishly that everyone within half a mile can smell it strongly. While I was perusing the meat section at the market today, one of the women strolling in front of me reeked so badly that I could taste her perfume. This is not a Japanese thing though. It's something that seems to occur in all cultures.
Quite some years ago when my husband was studying Japanese in a language school in Shinjuku, he had the misfortune to be placed in a class with an Indian woman who splashed on gallons of liquid flower before the class. The classroom was small and the windows never opened so he was trapped in there with this sickeningly overpowering odor. He had a word with the teacher about it to see if he could change classes or if she could do something to circulate the air so that the suffocatingly strong smell wasn't trapped in the tiny room but the teacher wouldn't or couldn't do anything about it. In the end, my husband had to quit the class because he was getting sick from the perfume.
It's interesting to note that people (mostly women) don't seem to understand that too much of a "nice" smell is as bad or worse than too much of certain types of bad ones. If I had a choice to be locked in a room with the men with B.O. or the women with the choking perfume, I'd probably take the B.O.