In AD&D 2nd edition, the rules for specialist wizards specify that each school of magic has one or more opposition schools, indicated via a diagram and a table in the Player's Handbook (in the 2nd printing, these are on page 45).
It isn't clear why the particular schools are opposed directly (that is, in the diagram, e.g. Illusion opposes Necromancy), nor why, in the cases where the schools on either side are also disallowed, why those schools.
The only explanation I found in the text says that the schools may be disallowed "due to the nature of the character's school. For example, an invoker cannot learn enchantment/charm or conjuration/summoning spells" but I don't see how that follows, and even if that were obvious, it doesn't explain the other oppositions (since, for instance, a conjurer can learn invocation spells).
I'm considering changing the opposition schools in the following way: divide the eight schools into pairs, and each pair opposes one of the other pairs.
Illusion and Enchantment/Charm are opposed to Alteration and Conjuration/Summoning.
Necromancy and Invocation/Evocation are opposed to Greater Divination and Abjuration.
In this way all the specialties will have exactly two opposed schools, and the opposition is always mutual.
Could this unbalance the game? I'd be fine if it makes an otherwise weak specialty stronger, or weakens a particularly strong school. But I'd be concerned if it weakened some school to being pointless, or strengthened one such that it's clearly better than the rest, or even made it stronger than some other class. I'm only using the core rules, so I don't have to worry about schools that only appear in supplements.