Also, Teddy is also a shit!
Deadbeat coward, didn't even get anything more than some random's word and ran off on his kid!
One thing I paid close attention to when rewriting Lexi a few years ago was making everyone in her life flawed. Despite nobody being a necessarily bad person (besides Randall, but even he has his reasons for being terrible), their worst choices unknowingly contributed to Lexi's fate. Which I think paints an interesting narrative, as when Lexi disappears, everyone blames themselves, yet for the wrong reasons.
Bonnie blames herself for not protecting Lexi enough, but she assumes she should have been protecting Lexi from herself. Allegra blames herself for rejecting Lexi's friendship, instead of acknowledging that the effects of her bullying were not so easily repaired. Teddy blames himself for not letting her stay, when he should have been blaming himself for leaving to begin with.
But why did he do that in the first place?
Just as a reminder, Teddy and Bonnie were both 17 when Lexi was born. They divorced six years later, at the age of 23. Teddy had to mature a lot, far too young and far too fast. However, his maturity was more of an illusion. Since he was far too busy working his ass off to keep his wife and daughter comfortable, he didn't really have the time to make sure he was maturing emotionally. So when he learned that the love of his life had cheated on him, he was shattered, and all that toughening up he had done over the last six years meant nothing. Getting a job and becoming more analytical was one thing, but keeping his emotions in check through intense emotional turmoil was another.
However, there were actually more reasons he left Lexi with Bonnie. Firstly, he assumed that Bonnie was already in a secret relationship with Randall and would now be free to be with him, which was confirmed when Bonnie married Randall a few months later. Which sorted the financial concern. Speaking of Randall, neither Bonnie nor Teddy knew what kind of person he was. Before the 'cheating', Randall was just Bonnie's easygoing, slightly lazy manager. Teddy didn't have any reason to assume that Randall was going to be abusive to his daughter, and wasn't around enough to notice. Nor did Lexi trust him enough to tell him.
Additionally, even in his grief, he was able to acknowledge that Bonnie and Lexi needed one another, and he loved both of them far too much to separate them. There's also the regular, mid-1990s deep-rooted misogyny that led society to immediately assume the mother is the best candidate to care for her children, regardless of who she is or the situation.
It's also important to note that Teddy didn't just completely disappear after he moved to Montana. Every birthday and Christmas, he would swing by to see Lexi, and every summer, Lexi would take a trip to Montana to stay with him. This was the case until she turned 13 and refused to see Teddy at all, which he chose to respect.
However, despite these reasons, Teddy could still have done better as a father. He could have demanded Lexi live with him once her disorders only worsened despite multiple drugs, therapists and psych ward stays. Or better yet, when someone literally attempted to murder her, nearly succeeded and left her hospitalised. He could have chosen to see Lexi anyway, despite her protests, and asked why she didn't want to see him, rather than assuming a 13-year-old could make well-adjusted decisions. Told her why he was leaving, instead of trying to "save" her from a reality she would learn later in life anyway.
Even though Teddy is an amazing father in Act 2, it was certainly a gained skill.