The second point you brought up is false. After the split it will not be possible to spend your coins twice on the same chain. The chains will have effectively split creating two separate currencies, it does not make double spends possible, for you to say that is just baseless fear mongering.
He doesn't mean spend the same coins twice on the same chain, he means that with two chains, the amount of Bitcoin you have essentially doubles. If you mix your prefork coins with post fork coins on both chains, then you have the same amount of currency on both chains. You have double of what you had originally and can thus spend more than what you should have been able to.
This is a good thing, it protects the users of Bitcoin, since regardless of what chain becomes dominant Bitcoin holders will have a share in both chains, making it a win win for users. Surely it would not be better if users had to choose? Making it a win lose proposition. This scenario would effectively split Bitcoin into two currencies, therefore it does not increase the total supply and does not weaken the value proposition of Bitcoin, from my perspective it actually strengthens it.