From a NY Times article by Dick Cavett - I'll preface it by saying that I was never a Godfrey fan and it's not my intent to defend him. Just trying to tell it like it was.
"There are two versions. One is that Arthur heartlessly, publicly fired a personable young singer — a member of the Godfrey “family” — live, on-the-air. So great was Godfrey’s size in the entertainment world that the dramatic phrase “the nation was shocked” is no exaggeration.
In fact, re-examining the incident, it’s hardly the unmitigated evil it was depicted as at the time. Not only had Godfrey and La Rosa previously talked about the young lad’s desire to move on, but the big bosses at CBS strongly urged Arthur to handle the parting on the air. Doing so, Arthur used the words “Julie’s swan song” and wished La Rosa well. Listening to it now, it seems both harmless and cordial."
I know that it is fact that LaRosa was looking elsewhere. He had a hit song and was looking to build on that. Godfrey's biographer hinted that LaRosa felt he was too big for the show.