Why are Jews called the chosen people? What makes them special and different from everybody else?
The term "chosen people" isn't something that orthodox Jews invented to label themselves, it is a textual reference to a status conferred by the divine (if one accepts the authority of the text in question). Why do Americans call America "the home of the brave"? Because there is a poem which uses that phrase about America and Americans see that poem as an accurate and authoritative statement about themselves.
Does this mean that America is "special" or just that Americans see it as having a particular position in their lives and their world view?
The term "chosen" seems to offend some people. And yet it doesn't mean "special" any more than a student who is "chosen" to go to an Ivy League college is "special" while someone going to any other school isn't. Or someone who feels a calling to go into politics vs. someone who stumbles into a life as a lawyer.
noone is more "special" than anyone else. some people have different jobs to do. if a nonjew does what he's supposed to do, he's considered among the righteous of the nations and has completely fulfilled his purpose.
this audio explains it much better than i could. Three flaws of Man - the role of the Jews. by Rabbi Uziel Milevsky O.B.M. former chief rabbi of mexico