Why boric acid (H3BO3) is a Lewis acid but not an Arrhenius acid?

According to Arrhenius theory an acid is a substance which produces H+ ion when dissolved in water. In the case of boric acid it does not produce H+ ions in water from itself but instead it produces H+ from water by acting as a Lewis acid. The boron in H3BO3 has sp2 hybridisation and there is a vacant p-orbital with boron which makes it a good Lewis acid.

Here, we can see that the boric acid is not producing H+ ion in water from its molecular unit. The water acts as a Lewis base here and it donates its lone pair of electron to the Lewis acid H3BO3. In order to stabilize the positive charge on water, it removes the H+ ion. This is the reason why ortho boric acid is not considered as Arrhenius acid. Instead it is considered as Lewis acid.