Some aspects of US are, indeed, the greatest. But, there will always be some that aren't, and even some that are the worst among the developed world.
US did not actually have the democracy/republic that its Constitution describes until about 1964, potentially a bit later (maybe 70s). Until then, minorities (esp. blacks), women, natives, they were all treated as lesser beings by the laws as well as by the people. So, certainly not all equals.
Nowadays, all of our freedoms are ever so slowly deteriorating. Usually, the tradeoff is a promise of safety. This is an old fairy tale, used in many other countries to deteriorate freedoms. You're better off less safe and more free than with promise of safety (mostly false) and much less freedom.
You're better off risking a terrorist bomb than giving away your rights and freedoms to privacy at airports and over telecommunications and Internet. There is a level of risk that will always be present and cannot be eliminated, so the promise of safety is a false one. The question is where to strike a good balance and the answer is that is must be struck at the point of civil rights violations, even if there are solutions that would give you a modicum more safety at the cost of many of those same rights.
Under the guise of keeping us safe, we can also adopt "us vs. them" attitude, which allows us to distance ourselves from fellow citizens who have broken one or more laws that we enacted for our safety and that violate our freedoms and rights.
This lets the govt dispose of the violator without much question and, sometimes, in a grossly inhumane way, while we avert our eyes telling ourselves that this can never be us -- this is THEM.
This is how a perpetrator wearing a police uniform can choke a man to death without resistance, and then walk away scot-free. We forget to treat them both equally and respect their rights equally. We see one as US, the other as THEM. We see a dubious character, and suddenly it is okay for them to die and perpetrator to walk away?
Until it happens to US. And then you are on "the other side", then you are THEM. Too late then. You must see it now, if you want to make changes.
We still enjoy a great deal of freedoms in this country, which still makes it one of the topmost democracies/republics, but freedom is a fickle thing and it can escape, and has done so in the past to the best of them.