My teacher said that you cannot stop fats going bad with freezing. So fatty meat is not good idea to freeze over a long time. Are there other factors to consider in freezing meat?
There is some truth to this. Fats go rancid, and in particular you're worried about rancidity due to oxidation here. Freezers do not stop oxidation, but they do slow it down a lot.
The main factors in oxidation are light, heat, and metal. Storing meat in a sealed freezer-safe (plastic) container or bag and using the smallest container possible will make the meat last a very long time - usually up to a year - before there is any noticeable rancidity.
Obviously, lean meats such as chicken breasts will last longer than fatty meats such as pork, since the fat is what oxidizes. Also, vacuum-sealing and/or the addition of antioxidants will practically prevent any significant oxidation - the former because oxidation needs oxygen, and the latter because the free radicals get absorbed before they can contribute to rancidity.
Another concern is freezer burn, which is also due to oxidation (along with dehydration). This is almost always caused by improper storage. It's only ever happened once in my freezer, and that was when I ran out of freezer bags and used a sandwich bag instead (so don't do that).
Practically, for meat, oxidation in the freezer isn't really isn't a big concern if the food is properly stored, because very few people freeze meat for that long. Plant products are different because they contain enzymes which give off ethylene gas, so exposure to anaerobic conditions (e.g. freezer storage) can lead to off colours and flavours. That's why pre-frozen fruits and vegetables have generally been blanched to kill the enzymes.
Anyway, back to meat - freezing doesn't change any "nutritional profile" other than the supposed food safety issues associated with rancidity. Just cook/eat it within a reasonable time and it's practically the same as fresh.