<p>As simple as plain HTML-CSS-powered website, CS / IT degree won’t teach that.
If you want to get deeper than that - like building the website using a particular framework (or using your own custom framework), or in general, doing databse-powered enterprise level you might want to have some classes related to database, fundemental stuff of computer science…
I personally do Django (Python web framework).
People don’t actually need to have CS degree to build a modern website (modrern i mean database-powered, dynamics, fancy, rich UI). </p>
<p>But if you want to open more opportunities for yourself, get a CS degree then. I am a computer engineering major, and I take CS classes. I am learning to make android app, and I think having knowledge in web development and have a good understanding of computer programming and computer science is very helpful.</p>
<p>I totally agree with RacinReaver. This is definitely a plus on your resume if you can write a good website. There is a lot involved in building a website. My suggestion is be patient when you learning. </p>
<p>Oh. Look through open sources projects written in PHP, such as phpBB, Drupal. Get to know them. Play around with them. They really help me to become a better CS student (I met them during my high school years).</p>