A "blanket statement" is one that covers everything like a blanket would. It usually means "overbroad", "too general", "not allowing exceptions." There are many different kinds of jazz, and when A says that she hates jazz, she's including ALL of them. This is a blanket statement. B probably thinks that this is unfair because A hasn't listened to all of the different types. Saying that every Korean likes kimchi is also a blanket statement because, by definition, it includes ALL Koreans. (Personally, I compliment the Korean people on their fine taste in food.)

Maybe because the person is basing their hate of jazz on just listening to one or very few jazz songs. You can't hate an entire genre based one limited knowledge. Similarly, you can't base you assessment of all of Korea's love of Kim chi based on what you know of only a small selection of people that you may have come into contact with. No one will ever know ALL of Korea. Nor will the know all jazz songs.