But that respect wasn't mutual, at least to start.
On The Boardroom: Out of Office, Taylor revealed he was concerned about Belichick's quick rise from assistant special teams coach to defensive coordinator of the New York Giants (via Jordan Cohn of Radio.com).
"The next year, he's special teams coach, and then the third year, (Bill) Parcells becomes the head coach and he makes ... Belichick the defensive coordinator," he said. "And I went apes--t. I went up to him and I said, 'Ain't no way! Ain't no way!'"
First impressions aside, Taylor said his former coach "turned out to be one of the best coaches in history," so there's some admiration on both sides these days.