The reason why Axew learnt Outrage in this episode is more complex than that. To understand all of this, you should go to a Trainer Yusuf post in Bulbagarden in the thread "the writers do enough with Iris" in the page 25 (it isn't exact). (it's posted just before Cynthia, he thought that Iris wouldn'0t cartch Dragonite).
The main reason why Axew learnt Outrage is because an animator can't contribute the show anymore, that episode would be the last episode that he made and apparently the animator want to do something special before he leaves the show.
If you see, the episode 42 of Best Wishes (Club Battle/Don Battle Part 4) was animated by Takagawa. THis animator is considered the best animator of the Pokemon anime. But he only appears in very few episodes. He did 4 episodes in early BW, with the last of them being that episode. This is apparently the last episode done by him in Best Wishes. Probably because she want to show his animation, he did the animation of Axew attak to make it like a departure.
Because that, the episode was made that way. Take note that starting here, we are going into the episodes produced after the earthquake, who has less money to do them and etc. and an animator with Tamagawa can't eb uin the show because it's so expensive compared to other cheaper animators that use stocked footage.
The attack, to show off, can't be stocked in future episodes. And remember, that if a attack can't be stocked in Best Wishes, you won't be saying the attack many times. That attack can't be used.
Because the animation of Outrage is so expensive, the writers don't want to showcase it. And because it, Axew is only using Dragon Rage except two times that he uses Giga Impact. Cheaper attacks that can be stocked.
Note: although many of us dislike it, if yopu want the attack to play again and again, you have to use the same animation again, again, again, again, again, again.
