Peter Weber's decision to self-sabotage and pick Madison and not Hannah Ann in The Bachelor finale can be explained with psychology. His desire to end the show in a relationship even though he was unprepared for one speaks to the flaws with the franchise and with himself.
When Madison left Peter in Australia, he was left with Hannah Ann or nobody. He had already been emotionally manipulated by his mother Barb to get engaged to Hannah Ann. To be in a committed relationship with someone is to feel a sense of belonging, and here Peter was with someone who loved him. He was given the option of being with Hannah Ann or being alone, so he chose the former. But over time, he realized that decision didn't make him happy. He struggled to understand why choosing love over nothing had not been the correct choice. Still, he knew he had to break up with Hannah Ann because he wasn't on the same page with her, to his mother's chagrin. Even though he likely realized it was best to take some time for himself, he couldn't shake the feeling that he needed to make this whole thing right in some way.
When Chris Harrison went to get Madison, it presented an opportunity for Peter to show that he hadn't failed as The Bachelor. It also gave Madison an opportunity to feel like she had "won" from this experience. They each tried to make it work, going against Barb's wishes - and obvious signs that they wouldn't be compatible in the real world. Not even two full days after the finale, they had ended their relationship as well.
The Bachelor set Peter up for failure. He was not ready for marriage, and yet he was starring in a show that encouraged him to get engaged. When it became apparent that none of the women were going to work for him long term, he didn't have the option to simply walk away. He needed to see this season through to the end, and that meant convincing himself that unhealthy relationships were in fact going to be successful.
By the time Peter had gotten down to his final three women, it was obvious he wasn't going to be married to any of them for a long period of time, much less engaged. This is how it plays out for many Bachelors. From an outsider's perspective, what may be obvious is often blinding to the man in the middle of it all.