How can aluminium oxide be called an acid?
The most basic definition of "acid" is that it is a proton donor (or one which accepts a lone pair)

All of this stuff is done in an aqueous medium, so we can assume that all aqueous ions and molecules are present. With this assumption (in this case, we are assuming that $\ce{OH-}$ is available to react), we get the following equation:

$$\ce{Al2O3 + OH- -&gt; 2AlO2- + H+}$$

Similarly, we get:

$$\ce{Al2O3 + 6H+ -&gt; 2Al^3+ + H2O}$$

where it is acting like a proton acceptor (base).