One definition of an acid is "an acid is a proton donor." Acids "are acids" because the H attached to the OH is easily detached. That is, acetic acid is CH3COOH and its the H on the OH (the COOH part) that ionizes as H^+ and leaves the CH3COO^- as the anion. All carboxylic acids have the COOH grouping and it's that H that comes off in each of them. The H of the OH group on phenols behaves the same way which leaves the C6H5O^- as the anion.
