First, the post I responded to did not claim that our militaries could reach parity. It claimed that China could conquer the US. That's impossible, preposterous even, and the only thing that could change that is the singularity, and if that happens all bets are off.
Second, even reaching parity is an immensely daunting proposition. If China were to start building ships and aircraft, the US would respond in kind. Right now there's a lot of overhead and waste in the procurement process, that waste would disappear if shit suddenly got real. Sure, we 'only' have 20 carrier groups right now, but there's no reason we can't have 40.
There's two main force multipliers I see that we have that China will never be able to catch up with us on. First, training and experience. The reason we keep a small military manpower-wise is because every US soldier is extremely well-trained. If China conscripted a percentage of their population, they could instantly have a larger army, but that army would then need to be trained in how to conduct modern warfare.
Second, alliances with other countries. The best air-to-air missile right now is the Meteor, it's being developed in Sweden and sold throughout Europe. If China started rising militarily, the US and Europe would immediately start cooperating to counter it by sharing technology.
The US has an enormous amount invested in its military dominance, it will not give that up at any cost. China could not reach parity slowly, as it would never catch up, and it can't reach it quickly, because we'd notice and respond appropriately. It would be such a huge drain on their economy that they'd abandon the effort.
The Soviets never even came close to parity in conventional force projection. The Chinese wouldn't either in a strategic arms race. Even if they did, they'd still never in a million years be able to conquer the US. As well try to conquer the Sun.