If you saw Game of Thrones' fifth episode "The Door", you'll know that Bran Stark ruins everything for a living. Like when his mother said to stop climbing towers and the results pretty much led to a country-wide war, or when he wasn't supposed to touch the roots of the weirwood to trigger a vision by himself, which cut his much-needed training short and killed major characters and animals (R.I.P. Hodor, Summer, The Three-Eyed Raven, Leaf, etc. etc.)
After Bran came out of the creepy vision of the Night King and his terrifying army of undead soldiers, the Three-Eyed Raven told Bran that he was no longer safe in the cave shielded by magic from the Children of the Forest and quickly added, “The time has come…for you to become me.” And everyone went nuts. People are taking this quite literally, and because of the quasi-time travel introduced into the show this season, many are saying that Bran IS the Three-Eyed Raven.
According to emerging fan theories, the second youngest Stark is meant to grow old and await the moment in which the timeline starts over, destined to train himself and possibly prevent the disastrous events of the future from happening. But they couldn't be any more wrong than they already are, because it is literally IMPOSSIBLE for Brandon Stark to be the Three-Eyed Raven.
The Three-Eyed Raven is Brynden Rivers, a Targaryen bastard legitimized by his father Aegon IV and Aegon's sixth mistress Melissa Blackwood. Known as the Bloodraven because of his albinism and unique wine-colored birthmark running the length of his throat to his cheek, Brynden had one eye and was thought to be a sorceror. The Bloodraven arguably had more eyes in King's Landing than Varys had 'little birds'. Brynden chose to take the Black over death when jailed after serving as Hand of the King, and went missing after ranging beyond the wall thirteen years after rising to the position of Lord Commander. Thought to be the last greenseer (a.k.a. wise people with the ability to have prophetic dreams and visions, in addition to the ability to warg) he waited in his cave in the Haunted Forest with the last of the Children of the Forest.
So while the two share horrendous injuries and greensight, Brynden Rivers does not have much else in common with Bran, let alone actually be an older version of the crippled Stark. The Three-Eyed Raven did not signal the start of Bran's transformation into him, he simply stated that Bran is destined to replace him after his death. Unless the writers and producers of Game of Thrones are seriously lazy and decide to change yet another cool event that did not need to be touched by their grubby hands, Brandon Stark is not and never will be the Three-Eyed Raven.