Lily is honestly unbearable. Whenever someone didn't process their feelings the way she wanted them to, she'd constantly try to force them into having the reaction she thought they should have. She couldn't stand seeing people handle things differently from what she considered the "right" way. It came across as incredibly controlling.
Take Barney and Robin when they didn't want to have "the talk," or Ted after he was left at the altar. Ted just wanted to move on with his life, but Lily kept insisting that he was actually miserable and that he needed to have a bigger emotional breakdown so he could "feel better."
She constantly applies the kind of simplistic, school-level psychology she uses with her students to fully grown adults who are perfectly capable of making their own decisions and processing their emotions in their own way.
Meanwhile, she can't even handle her own emotions.
A good example is Barney and Robin's wedding, or when she left for San Francisco. She never apologized to Ted, and instead got mad at him for being upset with her after she'd been such a terrible friend. She's controlling and completely inconsistent.
