Above all else, Slughorn valued people who he felt would be successful in the future, because he wanted to be able to influence them (or at least make people think he could influence them). I don't think that Slughorn particularly cared for any of the students in his club, beyond how they could benefit him. That's why he asked the children of influential members of Wizarding society, and the occasional extremely skilled non-connected person.

For this reason, he had to make the Slug Club look exclusive, because who would want to join an "exclusive" club that allows just anyone in? If you think about it, it's a lot like the popular crowd in high school. The exclusivity is what makes people popular. Without it, no one cares. While I may not necessarily agree with it, I can understand why Slughorn felt the need to be so selective. It also gives a man with a Napoleon complex the opportunity to exert control over helpless students, but I digress.

Samantha-Hope//Slytherin