Organic chemistry: why is the carboxyl group acidic?

Tutoring chemistry, concepts arise. The tutor mentions an idea behind the acidity of the carboxyl group.

In my previous post I mention the carboxylic acid functional group. Yet, why is the carboxyl group acidic?

The reason I’ve heard is that the carboxyl group, being -COOH, is a carbon double-bonded to one oxygen atom and then single-bonded with another. This leads to very high electronegativity centred on the C atom. The result: the electron theoretically shared between the O and the H atom is drawn much toward the O atom. From the outside, therefore, the H atom appears as an unshielded proton, which attracts the negative end of a polar solvent like water.

In turn, the solvent molecules surround the H nucleus, their negative sides towards it, and pull it from the O. Said H nucleus, being just a proton, is the active ingredient of acidity in the context.

Source:

Solomons, T.W. Graham. Organic Chemistry, fourth edition. Toronto: John Wiley & Sons, 1988.