Answer: Well...
Step-by-step explanation:
A very large concern during the cold war was the chance of there being a nuclear war. Both the Russians and Americans held control of the majority of nuclear warheads existing at the time, and naturally, with the Soviet Union being a communist nation, this reflected negatively on communists in the American public.
Another reason was during the cold war, Cuba was taken over into a communist rule. Considering Cuba was right on the US's doorstep, they potentially could launch missiles at Washington DC.
I just do want to note that communist aren't bad people, and communism is an ideal, not a community. In fact, many european countries are communist and socialist.