Is antiperspirant bad for you?

This was inspired by another question about using bleach as a deodorant, and a lot of people suggested different antiperspirants.

I’ve read in various places that there’s a theory about antiperspirant being bad for you, from causing problems with sweat glands to breast cancer. Of course no two sources ever seem to have the same information, and where one source will tell you it’s bad, another will tell you it’s harmless.

Though it does seem that stopping your body from excreting sweat isn’t necessarily a great thing. Sweating is how the body cools itself down, correct? So what effect does antiperspirant actually have on the body other than keeping you dry?