You will have to find a bird that already knows dive then you can train your animal dive after you, the hunter, has learned it in your beast training then you can train it to your pet.  I had the same issue with bite rank 9, I went and tamed a spider with it and kept it until it said I knew the skill, it will notify you in chat log, which only takes maybe 10 minutes at the most of fighting with your pet.  Then you can dismiss the creature you don't want and train your old pet the skill.