Playing the guitar well is a talent, it has little to do with education or being able to work with other people. If you agree with this then here it is.

Writing good songs is not a talent. Its a learned process. For you to write good songs individually you have to have some concept of how music is supposed to sound to become cool. If you personally can write a cool riff then can you write a harmony for it that will make it sound better. Can you write another part to follow it up with? If so then thats great, and if not you need to learn how. The best way for me to learn this was by trial and error. This is the same way I learned guitar. So I recommend just start writing things.

Your band can't write great songs as a band unless they have an understanding of what is stated in the paragraph above. You all have to be able to write your own songs (with the exception of the drummer as long as he understands dynamics, can solo like a mo fo, and understands harmony (teaching your drummer how to play bass is a good idea for harmonies).) Your songs will only be as good as the writing ability of the least qualified person in your band. The best thing that your band can do right now is jam free style at practice (again, learning by doing things.) Continue to develop your song writing skills indiviually in your free time, and try to keep other members motivated to do the same. Don't discredit ideas no matter how much you don't like it. It might not be cool to you but if the writter likes it then someone else will. No idea is a bad idea.

Good Musicains write good songs. Good bands write great songs.