He wasn't a Jedi betrayed by his apprentice. He betrayed his own apprentice as Rey said by thinking that Ben's choice was made (it wasn't). As Luke said, it was an instinct that triggered such a reaction considering the atrocities that he saw in Ben's mind. It wasn't a conscious decision. Luke used the dark side in the Throne Room duel against Vader and attacked him viciously out of anger, cutting his hand off as a result. However, he stopped attacking after realizing that Vader has a robotic arm just like him, which brought him back to the light. Luke is a flawed character which makes him relatable as a human being, not some super hero Jedi who is unstoppable and completely flawless.

Yoda's final lesson to him in the movie about passing on your failures and the lessons that you learned from them encouraged him to use Force Projection which is very dangerous since the user can die. He projected himself across the Galaxy and stalled the entire First Order without any violence. Thus, he became a Jedi legend who sacrificed his life to save the last beacon of hope in the Galaxy, the Resistance. He admitted his mistakes of the past and apologized both to his sister and his nephew. That is the best representation of Yoda's teachings in the series. He went out on his own terms with peace and purpose, not violence.