It is known that acid should be added to water and not the opposite because it results in an exothermic reaction.

Our stomach contains HCl, so why don't we explode when we drink water?

The hydrochloric acid in the stomach is already quite dilute; its pH is in fact no less than 1.5 so that at the extreme maximum there is only 0.03 molar hydrochloric acid.  And even that small amount is, of course, stabilized by being dissociated into solvated ions.  There is just not enough stuff to react violently.