Knowing a programming language allows you to control all aspects of a website - layout, styling and content. And it will provide you with more opportunity to get more work.
I design websites and I write in the programming language php. Most all my websites are dynamic and involves the use of mysql databases. This gives me a decided advantage when it comes to closing the deal on a website. When the client is relaying his/her needs to me I am able to ask the right questions that will help me to complete the project in less time and give the client exactly what they want.
I don't have to wait on a programmer to get caught up on another project before he can get to mine, and I don't have to explain to him over and over again what I'm wanting. I also don't have to make excuses to the client as to why the project is delayed.
And the best part about having fewer people involved in a website project is that there will be fewer people to divide the check up with.
I make more money designing websites than I do typing in content, so I let the client do that. But I don't want them typing their content in betwixt my code. CMS's are terrible. They look awful, they're too big and they're too complicated. So I wrote and designed my own type of "CMS" that allows my client to easily add, edit and delete their own content to any page on their website via an admin area. And the completed website looks and works exactly as I and the client want it to.
So, there is a distinct advantage in learning how to program. It gives you more control, more confidence and more money making opportunities. I believe that Web designers are better able to learn how to program than the other way around.
Programmers do not have any artistic sense or design skills. As long as they can type something into a query field and get the results they want, then it can be in basic black and white and they would be happy. They don't care about styling. But if you as a designer with your flare for creativity could learn to write code, you could design a website that would work as great as it looks.