This has nothing to do with exit, and suggesting otherwise implies bad faith on your part. (The exception is if you've literally never read anything like the remainder of this paragraph. In that case, you can demonstrate good faith by admitting here that your argument was faulty, and countering similar faulty "exit" arguments from open borders advocates in the future.) You can leave your job at any time, but when you do so you can't require another company to hire you, and it's blindingly obvious that changing this state of affairs would destroy some of the best companies. Right of exit, which I support, is protected by refugee treaties and free world military power. A huge wave of unskilled immigration is practically certain to weaken the US enough to increase, not reduce, the number of places like North Korea that are outside the US's military reach.

And your "Chinese or Indian citizen" example actually counters your own argument. Both countries have far too many people for the US to absorb, and both have also succeeded for the last three decades at raising living standards for their native people by more than would be possible via any achievable amount of brute-force migration to the US (though they have a lot more to do). Chinese and Indian "right to pursue happiness" has very little to do with US mass immigration policy; trade policy, technology transfer, Pax Americana, and the like have been far more relevant for a long time.

And even your "extreme example" fails spectacularly. I am Chinese, I voluntarily work for a Chinese-owned company, I've spent most of the last four years in and next to Shenzhen, and these years have been very good to me.

With all that said, I do support loosening restrictions on migration when doing so is actually positive-sum, and I think Chinese and Indian student immigration to the US frequently qualifies. But right now there's no way to push for that without simultaneously pushing for far-more-negative-sum policies.