How do acids and bases corrode iron?

Because Acids and Bases are all about hydrogen, and ionised hydrogen can corrode iron. All atoms consist of protons and electrons (and neutrons, but they are not part of this discussion) When Iron is corroded it's is actually being ionized and making new compounds like ironoxide. read more

Bases like NaOH and KOH are very corrosive to aluminum and can generate hazardous amounts of hydrogen when they do. Hot, concentrated caustic will corrode many metals because it is highly reducing and will dissolve their protective oxides and keep them from reforming. read more

Acid corrodes a nail, that is, the iron dissolves into the acid through the mechanism described above. It doesn't exactly make a nail rust, and it's important to be careful in wording such ideas. The dissolved metal can react with oxygen in the air or water to form rust. read more