I think web development has a bit of a bad rap these days in terms of complexity. Things have moved on a lot from the 90s when anyone could hack together a bit of HTML and your biggest worry was making it work in internet exploder.
Nowadays a web dev needs a firm grasp on SQL databases and what you can and can't do on them, ever more complex stylesheets, a scripting language like PHP, Javascript plus interpretations like JQuery or AJAX, HTML, XML, the graphics packages used to produce the look of the websites, plus a whole host of subsidiary technologies including networks and Linux if you want to set up your own server as well as email, flash development and actionscripting, and on and on. And things are only going to get more involved now that we're getting into decentralised networks via WebRTC and mobile integration. And you do need artistic chops.
Yes the depth mightn't be as focused as C or whatever, but the breadth is impressive and growing more so. If a C++ dev was sat down and told to make a fully dynamic website from scratch, aestheticalIy pleasing and with all the bells and whistles, they might be surprised at how much is happening behind the scenes. I agree with the subby that traditional schools aren't going to cut it anymore, you do not need high end maths for web development, maybe something vocational to get a good grounding and understanding of the concepts before just doing it yourself.