To me, the Asymmetry is quite intuitive, and it's that notion that Benatar is tryihg to appeal to. However, his formulation can get in the way. Some have seemed to have come away with the impression that Benatar is simply stipulating into existence. So, yes, you could turn it around and say instead that the absence of pain is not good and the absence of pleasure is bad. But according to this prior notion of asymmetry he's trying to appeal to, that would simply be incorrect.
The following occurred to me as one way to illustrate the intuitive notion that Benatar means to appeal to: Let's say you want to turn the heat up not because you're uncomfortably cold, but because it feels more cosy to you (pleasure). However, if you turn the heat up I will feel uncomfortably hot (pain). To begin with, we are each in a neutral state of neither pleasure nor pain (0/0) If you turn on the heat, we will be at (1/-1). But this (intuitively) is a worse state overall than we began with. If pain and pleasure were symmetrical, there would be nothing to decide between (0/0) and (1/-1). But because the lack of pain/discomfort is good and the lack of pleasure is not bad, there is an asymmetry.