One of the hardest things that you will ever have to do in life is tell a friend that the friendship is no longer wanted. It is never easy to tell someone that you have shared so many events with, and have developed a bond with, that it is over. It doesn't matter if it was a short friendship, or a best friend, or how much you actually care about the person in question. Ending a friendship is never easy, and it takes a lot of heart to actually go through with it. It isn't easy, but here are a few tips as to how you can go about ending it.
If you have tried talking the issues out, and nothing has changed, you probably need to cut that person off. There are a couple ways you can go about this, and you could either tell the friend it is over, or just let that person fade away. Chances are if you are seriously thinking about ending the friendship, you are probably not seeing this person as much anyway. Give it a week or so, and if your friend doesn't say anything, you might be able to fight the battle without firing a single shot.
However, if there is still contact between the two of you, you should tell them straight up that you are done with the friendship. Just ask your former friend to not text you, call you, or ask to hang out anymore. You are no longer friends, and tell that person why you don't want to hang out or be friends anymore. If your friend doesn't get it, just remind them of all the things that you needed changed, and weren't. Stick to your plan to end the friendship unless things change.
If you friend knows you are serious, and is willing to change, then go ahead and try to work things out if it seems like it would work. Otherwise just stick to your guns, and don't talk to your friend anymore. Try to keep things in perspective though, and don't end a friendship over a small fight, as friends will have those from time to time. If you feel like you are not getting anything out of the friendship, and you need to move on, move on.
Ending a friendship is never an easy thing to do. Not only do you not want to hurt anyone's feelings, you don't ever want something like that to happen to you. Empathy is a good thing in this case, but you have to look out for yourself first. Stay strong, and stick to your plan if you are going to end a friendship, and don't let your friend guilt you into coming back.