What is a "web designer"?
The field of website creation is a vast one, with many different skills needed to complete a single site, ranging from creative design, to imperative programming, to natural language content creation. With so many different skills needed, it is often hard to figure out what one should learn when trying to apply themselves to a certain role, for example that of a web designer.
In the end, every organisation has their own requirements, and each one may define the position "web designer" differently. There is no "one true" skill-set that such a person needs to know – one can focus on having a wide range of competencies, or focus on perfecting one skill, and each will open up different opportunities. So just study what you wish, and there is sure to be a place for you, somewhere.