When cutting into the hide, always have your blade facing away from the meat. If you cut directly down into the hide, you will push hair down into the meat. Personally, I always gut animals. For one, I use the offal such as the heart and liver and two, I like to know what the animals has been eating (sort of an autopsy) and 3, it makes the animal easier to manipulate for butchering on the ground. But, same principle, regardless. Run your knife down the spine with the blade facing away from the meat and start working down one side at a time. Be sure to cut the hide on the ankles before you get that far with the skinning. If you wait until you get there to cut around the ankles, you'll get hair on the meat.
You'll get better with experience. Small game hunting is a big experience builder. A lot of people have a difficult time skinning squirrels without getting hair on the meat, for example. Rabbits are much easier to skin, but their hair falls out so easily that it is easy to get hair on the meat so, same thing: skin lots of small game and get good at not getting hair on the meat and it will greatly improve your big game skinning. When I go rabbit and squirrel hunting, I usually volunteer to do all of the skinning and gutting and I almost always do it in the field rather than in a "controlled" environment. This improves your skills as well, not to mention ensures the freshest meat and easier skinning since the animal is still warm.
If you do get hair on the meat, all is not lost. Far from it. If you have the ability to dry age your meat, then 2-4 days on big game should provide enough drying of the surface and skin shrinkage for the hair to come off very easily. Check it out:
4 days of dry aging. Hair will not stick to the dry surface. (You can also peel the silverskin off with you hands with 0 meat loss).
I had these two rabbits recently that got some hair on them. I left them in my dry aging chamber for about 20 hours. The skin dried out just enough that the hair didn't stick. (I wouldn't recommend dry aging rabbits for much longer than that as the meat will just flat dry out. If you want to truly "age" the meat, you will want to hang them with their hide still attached.