Eric Dane’s official reason for leaving the show was to pursue other opportunities, and Chyler Leigh’s official reason was to spend time with her family. If I had to guess I’d say these are probably partial reasons.

If you rewatch season 8 Eric Dane is looking incredibly thin during the last few episodes- his struggles with addiction were very apparent on screen. Pompeo’s contract was rumored to be up, and Leigh expressed interest to Shonda about being the “main Grey” on Grey’s Anatomy, which Shonda didn’t go for. So, make of that what you will.

TLDR; while they both had official reasons for leaving, they probably had other reasons at play.