h2g2 The Hitchhiker's Guide to the Galaxy: Earth Edition

Deodorant merely deodorise, that is neutralise any smells that you maybe making. Anti-perspirants stop you from making any smells in the first place by blocking your sweat glands.
Strangely enough, your sweat glands are there for a reason, which is to excreate toxins from your body.
If you try to block that process, then your body will suffer an increase in toxins. This is very unfortunate as there are a lot of lymph glands in that very area, whose job it is to keep the body running smoothly.
Is it a coincidence that this is where a lot of breast cancer starts? I'm afraid not. You have a choice, sweat a lot and use a deodorant such as a deodorant stone/crystal which is non-toxic, or you can muck up your body cleaning system and run the risk of breast cancer.
Although, there are also other factors linked to breast cancer, such as genetic predisposition.