Barney began the show as a Lothario who used increasingly elaborate schemes to seduce women. For a while, Barney and Quinn appeared strong together and they were briefly engaged. It’s unfortunate the show didn’t further explore Barney’s relationship with Quinn, as they were both manipulators with similar outlooks on life.
In contrast, Robin was never meant to end up with Barney and the pair were incompatible, both fearing commitment.
Quinn was arguably the only romantic partner in HIMYM who could properly embrace Barney’s past while still putting him in his place. They were equally devious, with Quinn tricking him into paying for expensive “dates” at The Lusty Leopard. This event was a major factor in their breakup, but her actions served as fitting retribution for Barney’s terrible behavior towards women. They started on a precarious basis but quickly grew to understand and admire one another.
Barney didn’t need to emotionally manipulate her into dating him, unlike his final “Playbook” scheme/proposal to Robin. He had good reason to avoid Quinn for deceiving him, but she positively challenged him. Barney and Quinn proved how well-matched they were when they pranked the gang, who were apprehensive about the couple. To teach them not to meddle in their relationship.
Barney and Quinn were both stubborn, but they also recognized their faults and strove to make changes for each other. They weren’t the most trustworthy of couples in How I Met Your Mother, as evidenced by their need for a prenup. But their goals were more aligned than those of Barney and Robin. The latter story dragged out for too long, despite the many signs she would ultimately get back together with Ted. Each was afraid of intimacy and reluctant to openly discuss their feelings. Robin even proposed running away with Ted on her wedding day.
Quinn was also independent but appeared more open to commitment, bluntly telling Barney where she stood throughout their relationship.
Quinn’s more positive outlook suggested she was willing to actively make a marriage work long-term. Conversely, Robin constantly worried she was making a mistake with Barney And they rushed into an engagement. While blindly ignoring why their first relationship failed. How I Met Your Mother set Barney up for heartbreak with Robin. Returning him to his womanizing ways when he could have grown further had he married Quinn.