It was just not a good marriage. The Penguins were an offensive powerhouse, and to say that the star forwards (Lemieux, Stevens, Recchi) did not enjoy Bowman's grating personality and tedious attention to defense would be a major understatement. They were coming off winning the Stanley Cup, and going from the beloved Bob Johnson to the grumpy Bowman was asking for trouble. To Bowman's credit, he improved their defense by leaps and bounds; but the Penguins went out with the goal of repeating as Cup champions as a way to honor their late coach Johnson, and put aside their disdain for Bowman at least for that one season.
Bowman was notoriously quick to put his imprint on the roster. Mark Recchi was dealt for Rick Tocchet, partly due to Recchi's sliding defensive play and a stupid remark about how he believed "his +/- didn't matter." Paul Coffey was practically given away to Los Angeles, because to put it frankly, Coffey and Bowman mix as well as oil and water. For the defending champions to have their best defenseman and arguably their best winger dealt mid-way through the season, something had to give; in hindsight, Bowman sacrificed his relationship with the players in order to improve the team, especially defensively, and to add a physical edge.
A tough, defensive-minded coach like Scotty Bowman and a superstar forward like Mario Lemieux just didn't go well together. That's pretty much what happened, and it was only made worse by the Coffey and Recchi trades, especially considering Recchi was Mario's primary right wing for the previous 2+ seasons.
It wasn't the last time Bowman would clash with a star forward. His relationship with Sergei Fedorov, in Detroit, was strained, to say the least. Fedorov hated Bowman's system and the fact that Bowman would actually use him as a defenseman once in a while. Interestingly enough, they put their differences aside for the sake of winning, and boy, did they ever win. Fedorov grew into Bowman's most trusted forward, and was his go-to guy in almost every situation, winning 3 Stanley Cups, a Hart, and multiple Selke Trophies under his watch. Bowman also went out of his way to reward Fedorov for his loyalty; I remember reading about when Bowman told Fedorov that they had traded for Slava Fetisov. Apparently it was on the team plane, and Fedorov almost jumped through the ceiling.