Apocrine glands
Presence of apocrine glands sets armpits, anal-genital area and ears apart from the rest of the body surface. In addition to the watery eccrine sweat, apocrine glands produce yellowish milk-like composition. It does not smell much, but, allegedly, provides food for the actual odor producers. The stinky substances are believed to be their excrements.
Teleologically speaking, seems like it is not known what apocrine glands are for. Some authors assume their function is to create body odor. There are speculations that it may play certain role in social and sexual interactions. If so, it may be against the Nature's intention to cancel it.
How strong body odors might be evolutionary beneficial, and if they were, why people do all sorts of things to get rid of them (even consider suicide)? If armpit secretion plays some role in socialization, do odor producing organisms broadcast the message or jam it? And do deodorants make it any clearer? Let's not pretend we may have answers to those questions. Kill your body odor and see. If you don't like living without it, you can always get it back.
Note that (except for the specialized form producing earwax) apocrine glands are located in places where body parts rub together when we walk or run. It is only natural to suppose that apocrine secretion provide lubrication and protects the skin from infections.
Discovered lately has been anomalous apoeccrine gland (the name reflects that it reminds both eccrine and apocrine glands). You may want to look for this keyword on your own.