You're looking at this the wrong way, from the perspective of valence electrons, rather than paired spins. Al has 3 valence electrons, yes - but 2 of those valence electrons are paired with each other (they have opposite spins) in the s orbital. There is only electron in the p subshell with no other electron paired with it.
Another example: Neutral P has a configuration of 1s2, 2s2, 2p6, 3s2, 3p3. It has 3 unpaired electrons.
Another: Neutral S has a configuration of 1s2, 2s2, 2p6, 3s2, 3p4. It has 2 unpaired electrons.
Remember Hund's rule! The "pairing" refers to filled (paired) vs half-filled (unpaired) electrons.