Why does Scandium only exist in the 3+ ion

You can see that Scandium is in group 3 of the periodic table. This means that it has 3 valance electrons and will have an electronic configuration of [Ar] 3s2 3p1. In order to achieve a stable octet, you can see that removing 3 electrons will give it the electronic configuration of Ar, thus making Sc3+

Scandium will probably exist in the +2 and +1 state, they are just not very stable (If anyone definitively knows, I will be very interested). In the +1 state, it will have a stable filled 3s2 sub-shell and in the +2 state, it will have a stable(ish) half-filled 3s1 sub-shell. Scandium can also exist in higher oxidation states, but this cannot be achieved chemically as the energy needed to remove electrons from the stable octet would be too high.

I'm afraid it's not as simple as 'existing' as the 3+ ion. What is true is that in aqueous solution at most (possibly all - I'm not sure) pH values Sc (III) is the most stable oxidation state.

However there probably exist complexes with certain ligands for which other oxidation states of scandium are more stable. Unfortunately I can't explain the sort of factors which might stabilise other oxidation states cause you won't have covered it at A level.

You can see that Scandium is in group 3 of the periodic table. This means that it has 3 valance electrons and will have an electronic configuration of [Ar] 3s2 3p1. In order to achieve a stable octet, you can see that removing 3 electrons will give it the electronic configuration of Ar, thus making Sc3+

Scandium will probably exist in the +2 and +1 state, they are just not very stable (If anyone definitively knows, I will be very interested). In the +1 state, it will have a stable filled 3s2 sub-shell and in the +2 state, it will have a stable(ish) half-filled 3s1 sub-shell. Scandium can also exist in higher oxidation states, but this cannot be achieved chemically as the energy needed to remove electrons from the stable octet would be too high.