The answer is undoubtedly Game Freak Logic. However, if you take a look at some of the kicking moves, it kind of makes sense why Talonflame can't learn them.
- Blaze Kick - This one should be on it, but it seems to be reserved for Fighting types. Only Hitmonlee, Blaziken, Infernape, and Lucario can learn it.
- Double Kick - Yeah, I got nothing for this. It should be able to learn it.
- Jump Kick - This one makes perfect sense. If Talonflame missed, it wouldn't crash; it'd just fly away.
- High Jump Kick - Same thing.
- Low Kick - This move is supposed to be a tripping move, where a heavier foe would fall harder, and hurt themselves more. It might be difficult to trip an opponent while flying past them.
- Mega Kick - It's a bird. How much power can he have?
- Rolling Kick - It's flying, not spinning. It could do a barrel roll, but that's not really what it means.
- Triple Kick - It doesn't have three feet.
- Trop Kick - It's not a grass type.
Those are all the "kick" moves I could find...