For years the argument ran one way: Six Sigma shrinks variation, innovation needs variation, so one must smother the other. Most of the current discussion has moved on to a more useful question: which work in a company deserves tight control, which deserves room to wander, and how do you keep one scoreboard from judging both? The answer is a division of labour with rules for handing ideas across, and it is something a Black Belt can set up in practice.

Why did Six Sigma and innovation start out as rivals?
The quarrel comes from what each side treats as the enemy. Six Sigma treats variation as the enemy: if every invoice, part or call behaves the same way, defects fall and the process becomes predictable. Innovation treats sameness as the enemy: a company that only repeats what it already does has nothing new to sell. Put those two instincts in one meeting and each hears the other as a threat.
The words are also part of the problem. Six Sigma has a firm definition: a data-driven method for finding the causes of defects and removing them. Innovation has none. It can mean a new product, a new business model, a new way of delivering an old service, or a small tweak that saves a minute. When one side has a rulebook and the other has a mood, the rulebook usually wins the budget meeting, and the people who came to invent something go home feeling audited.
What has shifted in the debate
Three things have changed how people talk about it.