Can we just talk about this scene for a minute? This is Lin Bei Fong, badass chief of police and daughter of the greatest earthbender, in an incredibly vulnerable moment. She’s just lost her metalbending force, she was defeated in battle (and only made it out safely because of Asami) and her career is pretty much going down the toilet. And here she is, admitting her failures and baring her soul to her ex-lover who left her for another woman. I mean, even with all their history and likely bitter break up, she still trusts him so much because there’s no one else in the world who knows her better than Tenzin. They grew up together, they both have the weight of their parents’ legacies on their shoulders and had an important relationship, even if it’s long over.
And notice Tenzin’s body language - Lin is lying down injured. Any normal people would kneel to be on level with them but Tenzin just stands there, keeping this huge distance. I think he feels like he has to maintain this space between them cause he knows how much he’s hurt her in the past and maybe he doesn’t feel like he has the right to come closer anymore. He knows what the police force means to her. She said earlier in the episode that keeping Republic City safe is the only thing she cares about, and maybe that’s the reason why their relationship failed? Or maybe it was because Tenzin left her that she’s now dedicated her whole life to being chief. Either way, at one point in their lives, she obviously cared about Tenzin a lot and I think she still does.