I'm going to start this off by saying straight up Braviary is not broken. Feel free to read the rest of this post at your leisure, but it's just going to be a tl;dr rehash of the arguments pretty much.
As leader of NU, I had a lot of discussions with a lot of people about the suspect process as a whole. I'm not going to sit here and argue the merits of it, but I bring it up for one specific point: when do we ban a Pokemon? As the suspect process is set up currently, voters are encouraged to vote Do Not Ban if they are unsure of a suspect's placement instead of Abstain. The reasoning behind this is if a suspect does not leave a large enough imprint on the tier for a qualified voter to form a strong opinion one way or the other on it, it probably isn't that large of a threat. Voting to ban is reserved for the overwhelming case where a suspect 100% dominates a metagame, to the point where you could still lose even if you don't fully prepare for it. The best example I know of was Staraptor in DPP UU. Despite its checks, it still dominated the tier until its ban.
I'm not trying to compare Staraptor to Braviary, or compare Braviary to Jynx or Gorebyss or Cincinno. To do so would be an unbalanced argument, since specifically in BW NU, we haven't had a suspect like Braviary yet.
Everybody in this thread and in other threads who have argued for Braviary's banning tend to look at Braviary in a vacuum. I'm not going to sit here and deny that Braviary is a great Pokemon in this metagame. I'm also not going to sit here and deny that if you don't take proper precautions for any top threat in NU, you will get beat.
Braviary has 3 legitimate sets it can use, each with different checks and counters. I understand that if you predict wrong, you're gonna have a bad time. However, I can say that about a bunch of Pokemon in this tier. If you predict Samurott's set wrong, you're probably going to lose a Pokemon. If you predict Gardevoir's set wrong, you're probably going to lose a Pokemon. If you predict Gorebyss's set wrong, you're probably going to lose a Pokemon. That's just the way the game is. Braviary doesn't do one thing so well that nothing in the tier can stop it, it does a few things pretty damn good.
It may sound like I'm underestimating Braviary's power or usefulness, but again, I'm not. I've been on the receiving end of a couple BU Braviary sweeps, and I've gotten a couple too. If you allow it to set up, be it through poor play or unpreparedness, you're going to lose. I can say this about any set up Pokemon though! I haven't seen anyone argue that Braviary can set up way more than it should be able to, in spite of the opponent's best efforts, because it simply is not true.
Before I wrap this post up, I just want to quickly touch upon the argument that Braviary makes stall not viable. This simply is not true, as a few people have shown. Unfortunately in NU, we don't have defensive behemoths with great resistances and good support movesets. We have the leftovers from 4 other tiers. Also even if Braviary did make stall a poor choice to use, that shouldn't matter when considering a suspect's status. It's not our job to determine if a playstyle is or isn't viable in the presence of a certain Pokemon.
It's our job to focus on the Pokemon's effect in the metagame as a whole. And on the whole, Braviary just isn't broken.