Being able to make things for the web... Ah, what a delightful skill it is. Anyone can do it. Web design has one of the lowest entry costs of any hobby or profession in history, and the potential for what you can create is vast, even limitless.
As the world becomes familiar with the web, and more comfortable with digital interactions, we begin to see the potential of the web for practical applications. It's not for nerds anymore—it hasn't been for a long time (a "long time" in internet terms, that is.)
Think about how much simpler people's lives could become with the thoughtful application of the web. If that sounds good to you, then you might just be a web designer.