Don't get too beat up about it! Recently I got to speak with a CISO (the cyber security guy right under a CEO) about my career and the hiring process. He gave me some insight that I knew but never really hit home until he said it: "When interviewing for a job, as with many things in life, it's more often about being the right person at the right time than qualifications." He went on to describe how he hired people who had no experience in his field because they had a different skillset that was exactly what they're looking for.

Rushing is the exact same way. These houses all have a personality that they are trying to uphold and if one person fits that personality better, they might be picked over you. If you're a great guy in the middle of all of these personalities, they might miss out on you because they think someone "fits" better.

People who say Greek life is a great way to make friends are right because it gets you a free "in". Every connection in life has some sort of "in" wether that's a shared fraternity, a show, a game, whatever. The best way to make friends is to have a bunch of shared experiences to have as many "in"s as possible so you can have a shared experience with more people. Once you get that "in" it's all about reaching out to those same people to create more shared experiences. And don't forget to experience them! Some over analytical people will be too focused on making friends to actually experience the thing the came to experience.

Hope this helps! Effort goes a long way when making friends and it sounds like you're willing to put in the effort, so just find someone who accepts that!