I just got a nice Azelf, but to cover everything properly, Focus blast would have been pretty nice since I can't make it learn tutor moves from Pkmn White 2 (Signal beam). And it is known as the Willpower Pokemon. In my opinion, it should have even been able to learn Aurasphere. Can someone explain me?
Mainly because Azelf is Psychic type therefore, fighting type moves aren't guaranteed to be in it's moveset. The only fighting type move it can learn is Detect but that isn't going to help. Sorry.
You will just have to switch to a good fighting type (if you have one) if faced with a disadvantage. I recommend Scrafty or Mienshao.
Look at the bottom of these pages for how to obtain them in Black/White 2:
That's your opinion, not Game Freak's. Unless you designed the games, I don't think opinions count for much.
This is also why you have a team of 6 Pokemon in order to achieve coverage.
Just GameFreak logic. They wanted it like that. Nothing more to say.