Earlier quoted context omitted.
The difference is that every country with any sense actually keeps track of its citizens. Consistently. Because when you say it out loud, it sounds ridiculous to be a government with no idea who your people actually are. For half a century social security cards had "not for identification" written on them because they are really bad for ID. Didn't stop everyone from using them as ID because there was no other option…
"Because when you say it out loud, it sounds ridiculous to be a government with no idea who your people actually are." In the US, one of the founding principles, different from all (almost all?) others at the time, was the people create the government to govern for them. Government was not suppose to be a system where the government (ie. the monarchy) rules and owns the people. I don't think it is such a bad idea tha…
My major issue with the thought process that gets you to "having a national is a violation of my freedom" is that you only want to be invisible if the government is an actively hostile entity to you that you want to avoid. It is also the principal justification to the right to bear arms - you arm the citizens against a tyrannical government.
The problem is that in both cases - if you have a government that you want to hide from anonymously or a government you need to arm yourself against - you have a government you need to overthrow. You don't just exist in this state of armament or anonymity without taking action to depose the king and reclaim your liberty.
In both cases there are real, persistent, continuous costs of not having a centralized record of citizenry with secure id (because social security cards are not even close to secure) as there with keeping recreational firearms ownership so permissive. The former means people fall through the cracks and need to exert tremendous effort to prove they exist while the later costs life and limb all the time.
If US history has taught me anything (in regards to the history of most nations) its that when trying to preserve liberty its a fine line between disdainful paranoia and reasonable ambivalence. And American culture definitely falls towards the extreme on that spectrum in a, in my opinion, really unhealthy way. It just breeds controversy and arguments about ideology without anyone actually doing anything to improve the world they live in for either outcome... which is a generally common thread in US politics, to be fair.