It's true that bettas will spawn literally anywhere, given the right water conditions. But you must consider a number of things;
1. Bettas are fighters. If your male is aggressive, you may loose your female because she has nowhere to run. Even a rather non aggressive/vicious male may badly injure the female in such a small container.
2. a good full grown female IME can lay up to 1300 eggs (av. 1000 eggs..... trust me, I counted). In small containers, you need more wc. Preferably 2 - 3 times daily. Now, imagine all those tiny fry practically filling up the water .... how are you going to do wc, siphon out uneaten food, fry waste, etc. It's too much work.
1fish2fish has a good point - your climate in general. It's more difficult to adjust smaller jars to the needed conditions.
3. Fry will need space to grow. You must eventually move them to a large tank. If you're only breeding one pair and have a large tank, why go to all that trouble. Why not do yourself a favor and breed in the large tank?
Most Asian breeders I know breed in small bins and later pour a number of spawns into one big tub. They don't do it for the heck of it, but for a reason. So, again, I highly recommend that you breed in a rather large container/tank.
As for egg/fry eaters, well they exist. It is caused by a number of things as previously stated by others. But if you happen to have a natural "eater" and you badly want his genetics, you must artificial hatch the eggs (read bettysplendens). If the eggs are good, they will hatch. Otherwise they will fungus. If possible, I suggest you use a different male and make your life easier.