How can i convince my mom to let me buy an airsoft gun?

Well dude your mom just want to do what she thinks is best. Guns are not toys and although I play paint ball I regard my paint guns with respect and care. You can easily hurt some one or your self if you do not know how to handle a gun with care. If your mother is against guns in general you probably do not have much of a chance of getting one, how ever if you really want one learn to handle a gun properly and safely show her she could trust you with the toy you want.