Juan Pablo Montoya decided to quit Williams after a row at last year's French Grand Prix, according to technical director Patrick Head.
Head predicted Montoya would be a future world champion
Head said Montoya, who joins McLaren at the end of the season, lost his cool at Magny-Cours and had to be reprimanded at a team meeting.
"I think Juan was not impressed at having his knuckles rapped," Head said.
"And I know the decision to sign with McLaren was taken within a few days of that incident."
Head said the row was triggered when Montoya thought team-mate Ralf Schumacher had been given preferential treatment to go into the pits during the race on 6 July.
Head said Montoya launched a 10-minute tirade at team members over his car radio.
The Colombian was subsequently reprimanded at a meeting on the Wednesday after the race.
"Juan incorrectly thought we had notified Ralf of his actions and called Ralf in one lap early," Head said.
"So he was pretty strong on the radio abusing the team.
"And then I think he went into a bit of a sulk and backed
off and cruised to the end of the race and maybe finished 15 or 20 seconds behind Ralf.
"In fact, as it happened in that last bit of the race, Ralf
made a bit of an error and slipped wide.
"Had Juan been on his tail he probably could have taken advantage of it."
Ralf won the race from pole position in a Williams one-two for his second
"Verbally abusing the team continuously on the radio we didn't think was appropriate when the guys had worked their nuts off on the car and done some fantastic pitstops," Head added.
"Juan didn't like that very much. We did talk about it. We thought we couldn't have a situation where he pretty much accused everyone in the team from top to bottom of being incompetent twice.
"We called him in for a meeting in the factory on the Wednesday after the race.
"But the thing I think caused him problems was he was given a letter from Frank that said that behaviour wasn't acceptable and we wouldn't tolerate it in the future.
"I think he was happy enough being given a verbal but didn't like being given a written letter at the same time.
"And that put him in a mood. He's a very passionate person and he decided we were against him and that was quite a fruitful environment for McLaren to persuade him that his future lay elsewhere."
Montoya admitted at the launch of the new Williams last month that he had had disagreements with the team.
Head, who also predicted Montoya would be a future world champion, said the Colombian had never found it easy to finish behind his team-mate.
"Finishing second behind his team-mate does not make him a happy lad," he said.
"Juan is a passionate character and by virtue of that he sometimes makes impulsive decisions and comes to impulsive conclusions."
Team boss Frank Williams said he was sorry to lose the Colombian, who won two races last year and challenged for the title until the penultimate round.
"He's a great talent and we're sad to see him go," he said.