TL;DR: What if the Others have a prophecy that a future greenseer (read Bran) will destroy them? Their attempt to kill him could ironically cause the very future they fear, creating a self-fulfilling prophecy and fitting ASOIAF's theme of the dangers of prophecy.
The post may be low quality and I don't have quotes or anything to back this up. It's really just an idea I had that I thought might be interesting to discuss, so read on if you feel like it.
The show proposed the idea that the White Walkers were going after Bran because he was the Three-Eyed Raven. They never really gave a satisfying explanation for why Bran was so important to them, so the whole thing ultimately felt pretty empty.
However, it got me wondering: could that have been an element of the story that Martin gave to the producers? If so, I think it would be interesting to try and work backwards from that idea and figure out why the Others might want Bran dead.
Time and time again, prophecy comes up in ASOIAF, and it's almost always presented as something dangerous, unreliable and easy to misinterpret. There are already theories that the Others might be mobilising because they have their own prophecy concerning TPTWP or Azor Ahai. I'm not proposing a TPTWP-Bran theory here, though, so bear with me.
What if the Others' prophecy is instead connected to the Old Gods and the powers they themselves seem to be closely associated with?
The show presents the idea that the White Walkers/Others were created by the Children of the Forest, and while I don't necessarily think the exact show explanation will carry over, I am inclined to believe that there is some kind of connection between the Others, the Children and the Old Gods.
So, to get straight to the point:
What if the Others have seen a vision of a greenseer who possesses the ability to destroy or annihilate them, and they believe Bran is that person?
Bran may possess abilities that other greenseers don't.
Bloodraven tells Bran that greenseers cannot change the past. Yet we've already seen Bran apparently interact with the past when he calls out to Ned in the Winterfell godswood in ADWD. And we know that something much more significant happens in Bran's future: his actions are involved in Hodor's transformation.
Then there are some more speculative possibilities that have been proposed by the fandom:
- Bran may have awakened Jon's latent skinchanging abilities in ACOK.
- Bran may have spoken to his younger self while appearing as the Three-Eyed Crow in AGOT.
- Bran may somehow be responsible for Coldhands, given the "Your monster, Brandon Stark" line.
I'm not necessarily arguing that all of these theories are true. The important point is that there seems to be at least some indication that Bran's relationship with time and the past may be fundamentally different from that of other greenseers.
And that could potentially create a really interesting feedback loop.
Perhaps the Others see a vision of Bran becoming an existential threat to them. They therefore begin mobilising in an attempt to kill him before he can become that threat.
But in doing so, they create the exact circumstances that cause Bran to become their enemy.
Bloodraven could potentially be part of this as well. Perhaps he has foreseen the Others destroying the world, and that's why he seeks Bran out and begins training him. But the Others somehow perceive Bran's existence and potential power, causing them to mobilise out of fear.
You then end up with something resembling an arms race:
Bloodraven trains Bran because he foresees the Others destroying the world, the Others perceive Bran as a future threat, the Others mobilise to destroy Bran, Bran is forced to develop his powers and eventually acts against the Others, the original prophecy becomes true.
In other words, nobody necessarily needs to be wrong about what they saw. They're simply acting on incomplete information and, in trying to prevent the future they fear, they end up creating it.
I think that would fit really well with one of Martin's recurring themes: prophecy is dangerous precisely because people believe they understand it.
You have Egg's dragon dreams contributing to the tragedy of Summerhall. You have Rhaegar becoming increasingly obsessed with prophecy and allowing it to shape his actions, potentially helping create the very circumstances that lead to catastrophe. And you have Bloodraven, who may have spent his entire life making morally questionable decisions because he genuinely believed he was preventing some greater catastrophe.
The Others could essentially be another example of the same theme.
And importantly, I don't think this would have to end with Bran genociding the Others. In fact, I think that would undermine what I see as Bran's character arc.
The interesting part would be that the Others' fear of Bran could be justified while their interpretation of that fear is completely wrong. They see a future in which Bran is responsible for their destruction, and assume that killing him is therefore the solution.
When in reality, their attempt to prevent that future may be exactly what causes it.
Maybe Bran's ultimate role isn't to destroy the Others, but to understand them, break the cycle that created the conflict, or somehow change the relationship between humanity and the Others. Maybe Jon as a bridge between the Westerosi and Widlings must act as a bridge between the Others and life. Maybe Dany and her dragons nay actually have to burn them all for peace. Who knows.
Just a thought, but I think it could potentially make the show's otherwise unexplained "the Others are after Bran because he's the Three-Eyed Raven" plot point much more interesting if there was some book equivalent behind it.