Now to come to the question: Can you teach yourself piano? Of course, you can. The only problem is that most people will only do their own teaching ever so often, and never really develop or finish any piece of music unless they are highly motivated and disciplined!
The piano is one of the most difficult and rewarding instruments to learn; not only do you have to learn to read notes and translate them to the keys, but you have to do it with both hands at the same time. You'll also have to learn to play with the correct technique or you could face injuries in the future.