First, and foremost, if you are a writer then you need an audience. If you are reading this article then you know there is a huge audience accessing their reading material via the Internet. Unlike the reading audience of traditional printed materials, the Internet-reading audience is growing exponentially. More and more people are forgoing traditional newspapers, magazines, and books to subscribe to ezines, web pages, blogs, and RSS feeds. If you can find your audience on the Internet, then that is a very good reason to write for the web.
Another good reason for writers to transition to the web is that is where the money is today. While money can be made through the traditional avenues of publishing books, selling articles, or working as a writer for hire it is getting more and more difficult for established, proven writers to make a living and extremely difficult for newcomers to break in at a livable wage. However writers can start up their own business fast and cheap or work for hire to learn the ropes and build up their nest egg. Trying to do either of those things in the traditional publishing world will not find success.
Finally, or third, there is a niche for everyone on the Internet. Most traditional publishing methods are limited to a specific region due to the cost of printing and distribution. However neither is a consideration on the Internet, so writers can reach audiences around the globe. This means that what may seem a rather small niche (of say people who collect dachsund sweaters) may well find their audience is hundreds, thousands, or even millions. That means there is a need for articles and publications for these folks. As an avid dachsund sweater collector yourself you are an ideal writer for any publications currently serving this niche and if there aren't any then you have a wide-open field to start your own.
These three simple reasons should be enough for any writer to consider writing for the web. The Internet is a great place to break in and get started as a professional writer and the Internet is an even better place for the established pro to profit.