I don't think his point is that it isn't cathartic; he's pointing out that there is no physiological reason for crying in particular to have evolved to be cathartic. What have leaking eyes or a quavering respiratory system got to do with relieving overwhelming emotions? Nothing. And no other animals experience this.
It's a confusion of cause and effect (or post-hoc fallacy). "I cry because it makes me feel better" supposes that feeling better is the purpose of crying. But really it's the other way around: Crying is the purpose of feeling better. Crying is the thing with purpose, because it's an important and useful social signal. Overpowering urges to succumb to it, and feeling better after having done so, are evolution's way of coaxing our minds to do something that's useful to us, just like urges to eat or have sex, and feeling better after having done them.
It's not really a confusion of cause and effect. It's that most probably there's a cause-and-effect somewhere we don't know. America the landmass did exist before we got to know that it did.
It's quite suggestive that most of the nervous situations can lead up to physiological phaenomena like crying, laughing or stomach pain.
Why do we smile when we're happy? Is it because we're happy (we also expose a similar face when we're scared), or is smiling the purpose of feeling happy?
Not sure if you're arguing for or against my point, but I'd say the purpose of feeling happy is to reinforce the behavior that got you where you are. Smiling (and the compulsion to smile, which few other animals have, though they do feel pleasure) is to signal your state of mind to your peers.
I wouldn't say (and wasn't saying) that the purpose of feeling sad is to cry or engender social signaling (parallel to happiness, the purpose of sadness is downregulation of behavior), but the compulsion to cry itself and the relief afterwards is about signaling.
It's a confusion of cause and effect (or post-hoc fallacy). "I cry because it makes me feel better" supposes that feeling better is the purpose of crying. But really it's the other way around: Crying is the purpose of feeling better. Crying is the thing with purpose, because it's an important and useful social signal. Overpowering urges to succumb to it, and feeling better after having done so, are evolution's way of coaxing our minds to do something that's useful to us, just like urges to eat or have sex, and feeling better after having done them.