Bran the Broken: the child who would fall from a window and rise to rule Westeros. What a heroic character arc. Except, it isn't really. Brandon Stark, fourth child and second legitimate sone of Ned and Catelyn Stark, may have started out as an adorable underdog, but his actions as the Game of Thrones series continued became much more self-serving and much less understandable to both those around him and the audience of the series.
For a while at least Bran meant well. Some of his worst moments maybe just frustration and the petulant acts of a young child but Bran was far from a perfect example of heroism and leadership.
He's Rude To Old Nan
Poor Old Nan is left to look after a bedridden Bran when his mother, Catelyn, leaves for Kings Landing to discuss the most recent murder attempt on their middle son with her husband. She just wants to keep him occupied, tell him stories, get him something to eat if he needs it. Bran yells at her, tells her he hates her stories. If he likes any of them it's the scary ones. To which Old Nan explains that he, Bran, is a summer child and knows nothing of fear. This does not make him any more respectful or kind to the old woman caring for him.
He's Rude To Maester Luwin
In the same way that Bran cops an attitude with Old Nan he is less than respectful to his teacher and caregiver, Maester Luwin. Bran is, of course, upset that his mother has left Winterfell but that doesn't mean he needs to be rude to anyone and everyone who is trying to protect him in her absence. Still, despite Maester Luwin's patience Bran continues to ignore his questions, the lessons he is trying to teach, and hold the disappearance of his mother against the old man.
Disobeys His Mother
So many terrible things could have been avoided if Bran had kept the promise he'd made to his mother, Cately Stark, that he would not climb up the outer towers of the Winterfell keep any more. Of course, he did and, in doing so, came upon Jaime and Cersei Lannister and their incest. This led not only to Bran being pushed from the tower by Jaime, but later to another attempted murder on his person, forcing his mother to head for King's Landing, and eventually the full and murderous feud between the Starks and the Lannisters and so much bloodshed.
Possessing Hodor
The first time it is an accident. When Bran, along with Meera and Jojen, are trying to keep Hodor quiet so they are not found while in hiding, he wargs into Hodor's head, making the giant man pass out.
This is a rare gift, taking over the mind of a person, Jojen explains. Taking over anyone's self-control, even Hodor's is not a great look. Autonomy should be respected and, when Bran uses Hodor again, this time as a fighting machine, it's clear even Hodor is upset about it.
Yields Winterfell To Theon
Of course, Bran is a child, and he yields his home to Theon believing it will keep him and his people safe. This, we know, is not the case. One actually wonders what worse things Theon could have done had Bran not yielded to him. Burn the whole keep down with everyone inside perhaps? But then what would there have been for young Theon to rule over. Instead, Bran's yielding of power only leads to Sir Rodrick's death, the death of two orphans, and the eventual partial destruction of his home anyway.
Uses Greensight Without The Three Eyed Raven
When learning from The Three Eyed Raven, Bran wakes up in the night and decides he wants to touch the roots of the wierwood and take a little trip of his own. This vision takes him to view the armies of the Night King and the Night King himself. The Night King makes a grab for Bran's arm. When Bran returns to the present The Three Eyed Raven knows that the Night King has touched Bran and thus all the magical protection that once surrounded the cave where they are all staying has disappeared.
Abandoning Meera
The real hero of the Bran Stark story is Meera Reed. Not only does she sacrifice her brother Jojen so that Bran can make it to The Three Eyed Raven, she is also the only one left when their magical cave and wierwood is burned. That means that Meera stays with Bran, protects him by herself, and drags him, on a sled, singlehandedly, back to The Wall and the rest of Westeros. What does she get form Bran for this faithful service? Nothing. He gives her a lame thank you and sends her on her way.
Bran Lingers In The Past
Bran, as is apparent when he goes off on his own, wants nothing more than information, the more the better.
This does not only lead to the Night King finding him and his friends, but it also leads to his friends having to fight without him. When the weirwood cave is attacked by the White Walkers Bran's eyes are fogged and he remains watching his father in the past, his father and Hodor.
Created Hodor
Watching Hodor in the past, where his father, and uncle, and aunt Lyanna were still alive, doesn't just lead to Hodor's death in the present, but the ruination of Hodor's mind in the past. As Hodor fights to keep the walkers from reaching Meera and Bran he is forced to "Hold the door." With Bran's presence in the past Hodor's mind falters, combining his present fight with his past self and leaving nothing but his experience of "Hold the door," behind. Thus the boy becomes Hodor.
Sat Out The Battle Of Winterfell
Fans watched Bran learn to see the past and the future. They watched him learn to use his greensight and warg into both animals (like ravens) and people (like Hodor). The fact that as The Three Eyed Raven, Bran has incredible power was never in doubt. What was horrible and confusing was to watch the powerful Three Eyed Raven sit in the Godswood during the Battle of Winterfell while family and friends fell all around him and do nothing.