The moment you make an argument personal is the moment you lose it.
If your position is right because the other is wrong, or is an idiot, or did not do a good enough job, or is not as competent, your position is extremely weak. And even if you are right, there’s no way you can prove them wrong.
Keep discussions around facts instead and be ready to accept other opinions as valid and worth your consideration.
Arguments are negotiations, and no negotiation can leave one party empty-handed.