I think Jeff Morrow is right about the sentence being "convoluted". The same idea can be conveyed in a much simpler way. Given that it is from a TED talk, I presume it was rehearsed.
From Cambridge, "insist" means "to say firmly or demand forcefully."
The speaker has many stories, many experiences - some negative and some positive. All of that have shaped him into what he is today. Assume that the speaker is someone who is successful, inspirational, a survivor, a fighter, etc.
The speaker is saying that asking him about [or insisting to hear] only his "negative experiences" - to understand how he became what he is today - forms a misleading narrative. Negative life experiences such as growing up in poverty, losing his parents at a young age, having to live on the streets, academic and business failures, have all significantly contributed to his success. But they are not the only experiences that have made him successful. He was able to get into an Ivy League university, where he was taught by the world's best teachers. They inspired him and empowered him to be able to follow his dreams. The speaker wants people to ask him about these positive stories because they are just as important to him as his struggles.
The single story creates stereotypes, and the problem with stereotypes is not that they are untrue, but that they are incomplete.
This might be an extreme example but it helps to understand this.
Failure is the key to success.
That is incomplete. It is the hard work and perseverance (after the failure) that is the key to success.
Everyone thinks that Mike Tyson, one of the greatest boxers of all time, was great because he had nothing, he had no parents, no house, and no relatives. They think Tyson was great because he was "hungry". They think he became a champion because he grew up in poverty. And because he had the darkness and the desire to kill. All that significantly contributed to him becoming a fierce fighter and the youngest heavy-weight champion of the world. But to say only those struggles and "negative experiences" made him what he was, would be wrong. Tyson had one of the greatest coaches ever. He was taught one of the most difficult-to-counter boxing styles of all time. Tyson loved his coach like he was his father. His coach was the reason he had a roof over his head and had food on the table. Without his coach and his coaching team, Tyson wouldn't be a champion. A person in Tyson's place, would want his positive stories to be heard as much as his negative ones.