It's because of comedy, and the people that don't understand what comedy or a sense of humor is. The term Jew has, for several years, been used in comedy when referencing the holocaust. Since comedians and people have been joking about it, others have taken offense to it. This only fuels the fire, and now the word Jew is a slur for a Jewish person.
As Louis C.K. said, "Jew, is the only word that is the right thing to call a person, and a slur for the same person! You can say, 'he's a jew', and it's fine, but if you say it, 'he's a jew', its a terrible thing to call a person!"
Other religions have different words that are slurs for their people, but Jew's got seriously unlucky and it ended up being the same word.