I have someone I consider a best friend, but she tells me that she already has a best friend. She says I'm her friend, and even a close friend, but it bothers me that I consider her my best friend but she doesn't do the same. Is this a good friendship? Should I leave?
If you're enjoying your friendship, you definitely don't need to leave it. Not every friendship is going to be the same.
The short answer is the yes, you can have a best friend that you cherish who doesn't consider you their best pal in return. That doesn't mean that the person doesn't consider you a good friend, it simply means that there might be someone else in their life that they are closer to.
This type of relationship isn't a one-sided friendship necessarily, where one person puts all the effort into the friendship. Instead, it typically occurs when one friend has more pals than the other, or just has a closer relationship with someone else. You can still have a very fulfilling friendship with someone you consider a best friend, even if they don't think of you the same way back.
A fictional example of this type of relationship is on The Office, where Dwight considers Michael his best friend. Michael, in turn, doesn't consider Dwight his best pal, but still appreciates Dwight in his own way.
This friendship usually works best when both people are aware of the situation for what it is. One person is not trying to "force" the relationship and make it closer. Instead, they just accept that they have a best friend who is closer to someone else, but is still a positive influence in their life.