Who says Americans think we have the most freedom? We have a history of freedom, and especially religious freedom, was a big part of our founding when that was pretty hard to find in the world. We also tolerate freedom of speech in a broader definition than almost any other country. We also were founded on the premise that each individual can progress based on their own merit. They are not born into a class and held there. At the time of our founding most countries that people came from had royalty and more obvious levels of social classes. In America we are “all created equal” so we can climb the social classes. We don’t have to live down a debt of our fathers, or be attached to our surname legacy. We can branch out and make our own way and be judged by our own work.
When America was created a lot of these ideas were unique and special. Not that people before didn’t want these freedoms, but America wrote it down as a form of government. It truly was a special creation for it’s time.
Now, many countries have similar freedoms, one might argue that in some realms the United States is not as free as other countries. But, in many realms we are free in a way that is more extreme in the US than other places.