China had already picked Pakistan before 1962, but Pakistan was too stupid to capitalize on it. Most people today don't know that China invited Pakistan to join the 1962 War, but Pakistan was a complete idiot at the time and refused. I've heard Pakistani generals on TV, when they are (rarely) questioned on this point, they respond by saying that the Pakistani Army wasn't expecting war in 1962 and wasn't operationally prepared. But that's a ridiculous excuse on every level. Why wasn't the Army "prepared"? That's literally their entire job. And if you're not prepared for a joint-campaign in 1962, why bother starting a war alone 3 years later? The correct answer is that they were idiots.
Here's a couple of other examples of our stupidity: General Ayub (the idiot we had in charge) refused to start Pakistan's nuclear program in the 60s, when the Nobel Prize winning physicist Abdus Salam advised him to do so. (Ayub didn't think Pakistan would ever need nuclear weapons lolz.) Ayub was the same guy who in the 1965 War recalled the front-line general leading the armored offensive in the Chamb sector, right as we were about to cut off Kashmir from India, because he didn't like him, so he put his best friend in charge (who later also headed the 1971 debacle.) This delay stalled the entire offensive in 1965 (which up to that point was resulting in a decisive victory). This was the quality of our "generals" at the time.
Given all of the above, the question arises, why did China "pick" Pakistan? I think it's because of some key factors right after Independence which influenced Mao and Zhou Enlai's calculus. 1) Pakistan had accepted China's territorial claims right from the beginning and even gave away territory to China which we captured from India in 1947, without asking for anything in return. 2) Pakistan was one of the first countries to recognize PRC as the rightful government of China and ended relations with Taiwan. These two factors, I think, led China to the same conclusion early on, that Nixon-Kissinger reached later: Pakistanis may be childishly stupid at times, but we aren't duplicitous (well, at least not until we get backstabbed first, e.g. by America in the 90s, at which point, we will find a way to f*ck you over somehow lolz.)
In any case, it seems like the scale of stupidity is starting to tilt in our favor finally. As Pakistan has gotten smarter over time, India has gotten dumber. Case in point:
