It's not just acids and bases...other compounds do it too (ex. NaCl). Look at how they dissociate and which ions are found once they do. Specifically, look at the type of bond between the two ions (hint). What type of solvent is water and how might this play a role?
This is a little bit putting things on the head. By (Arrhenius) definition acids and bases are substances that dissociate in water producing either H+ or OH-. As dissociation is part of the definition, every substance that we classified as acid or base must be dissociating. In effect answer to the question "why those substances dissociate" is "because we have chosen substances that dissociate".