Do I get annoyed when people say "America is the best"?
No, not really. However...
American and its counterpart unamerican are meaningless terms, but often used with an emotional load.
In reality, the word American refers to a geographical area, period. Anyone who believes that their geographical area is the best the best the best or feels more virtuous on the basis of an accident of geography that they had no control of, is a brainwashed imbecile. And anyone who repeats this mantra to others, is trying to manipulate you for his benefit.
Now, he will come who will say that America did this, or America did that, and that's why America is great. Nothing could be further from the simple, blunt truth: the fact is that people do things, not countries -- remember, soil doesn't move or think -- and if you feel proud or virtuous because some other person that you don't know did something, then you are not feeling it for anything that you did. Now, your feelings are your choice, but let's drop the charade and stop pretending that others' achievements make you a better person, because they don't -- you're just cruising on the momentum of somebody else's achievements. And every minute you spend in complacency of others' deeds is a minute that you don't spend on your own true improvement as a person.
Oh, and by the way, you can replace American by any other nationality. Same tripe.
You don't love your country. You love your loved ones.