I didn't get one thing.

The implication was that he killed himself because of the effects of McCarthyism. The details were left vague, but the implication was that he was accused of some crime, not just a general sense that he has "unpatriotic" beliefs as was more frequently the case, that made him unable to work. He became despondent and killed himself. I say this because Babe asks Professor Biesenthal whether he thought his father was guilty. In most cases of McCarthyism, it was not a case of guilt or innocence. It was simply being blacklisted for having been actively sympathetic to communism. Complicating the simple narrative that McCarthyism was evil is that history has shown that many of the accused communist spies were found to have worked for the Soviet Union. As for the purposes of the movie, it is an example of Babe's father being a victim of government overreach while his brother, Doc, works for a violent arm of the government.