"The reason I got off the board as they got more and more into creating television shows and movies, it became more clear to me our paths were conflicting rather than converging," Iger said in an interview with CNBC "Mad Money" host Jim Cramer. "I just thought it was the right thing to do."
"The business is still relatively small for Apple, but meaningful for Disney, and it wasn't right," Iger continued.
Iger resigned from Apple's board of directors on Sept. 10, the day Apple announced the price and release date for its streaming service.
Apple plans to launch Apple TV+ on Nov. 1. It's a streaming service featuring Apple-created TV shows and video content that will run on iPhones, iPads, and other Apple products. It will cost $4.99 a month, but will be free for one year with new Apple products.
Disney's own streaming service, Disney+, will be released on Nov. 12 for $6.99 per month.
Competition in streaming is heating up. In addition to Disney and Apple, CNBC parent NBCUniversal plans to launch a service called Peacock in 2020, and AT&T's WarnerMedia is planning an additional service under the HBO brand name. Netflix is the current leader in the market with over 151 million paid subscribers.
Disney and Apple have had a close corporate relationship before they started competing for TV shows and streaming subscribers. Iger had a close relationship with Apple co-founder Steve Jobs, and Disney bought Jobs' other company, Pixar, in 2006. Iger said that before Jobs died in 2011, he asked Iger to take his seat on Apple's board. Iger even mused that if Jobs were still alive, the two companies might have merged.
Iger also noted that Apple continues distribute Disney content through iTunes as well as Disney apps, and praised Apple CEO Tim Cook.
"Tim has done a great job," Iger said. "No matter what direction you look, I think you'd conclude that company is one of the great companies of the world."