Why is the so called Jewish defense league harming the reputation of Jews by attacking freedom?

Because they falsely believe that the protect Jews by terrorist activities ostensibly in defense of Jew both in the West as well as in Israel. They have also attacked and killed Jewish opponents of Israeli policies. I recommend reading some of it's founde"rs Rabbi Meyer Kahane's books to get a real flavour and perhaps even get sick in the stomach.Under the Soviet Union they placed bombs in NYC when the Bolshoi Ballet came to visit.