Why can dissolution reactions (e.g. dissolution of calcium chloride) be exothermic?
The endothermicity (taking up heat) or exothermicity (giving off heat) depends on a balance of factors including the entropy change, the degree with which the ions become associated with water, and the possibility of actual chemical reactions.

The most notorious example is sulfuric acid, which reacts so strongly with water that it can actually boil the water, and spatter the acid, which is why one always adds the acid to the water(water as solvent) and precautionary measures (gloves and proper clothing) are needed to handle the reaction.