That’s not exactly what it says, though. She’s just afraid that following the same path as her father will lead her into too many situations where she may give in to hatred like him. And we actually SEE her being aggressive in the flashback to get the upper hand. Thus why Luke appears shocked and Leia appears sad.

The goal is to make Rey and Leia’s Jedi paths the same without directly stating it. Both of them instinctively use their aggressive feelings to gain the upper hand in a fight. Leia decides to follow her mother’s path so that she doesn’t have this temptation on a regular basis.

But, ultimately, the point would be EXACTLY what you stated. Leia should have continued to work on overcoming her nature. It sounds corny, but she just had to actively choose love in the moment like she ends up doing throughout her life. This is why she is so insistent on training Rey despite her heritage. They have the same journey, and Leia is trying to remedy where she went wrong herself. But also where she went wrong with Ben, sending him away instead of training him herself.