How do you make your self a true friend to your true friends?

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While some other people are seeking for true friends, I, on the other hand is looking for some ways to bring out the friendly side of me. I've got a lot of true friends but it seems like I really don't know how to maintain a friendship nor expand it. I'm always a cold and strict person and I would admit it. Whenever I'm not pleased with a friend's behavior, I tend to terminate the friendship at once without a second thought. Sometimes, I could even consider my self an anti-social because I seldom go with companions. I've always preferred doing things on my own. In a classroom situation for instance, if our teacher asks us to look for a partner for an activity, I feel irritated because I just don't want to work with a partner or with anyone else as it would only open up an opportunity for a heated misunderstanding or dispute. Some would even comment on my preference on being alone but I just don't seem to care. I never consider my self as a true friend because of my pessimism. Whenever friends would talk on some nice and exciting things to me, I would only kill their joys because I would likely point out the dark side of it and I really love to discourage them in some of their endeavours. I also like to turn down invitations from friends and I would just make a lot of reasons for my absence say, in a birthday gathering, meeting,etc. I know I've got to end this and I just don't know how.