That is an excellent question, Ryan. The main benefit of handcoding over using a WYSIWYG tool like Dreamweaver is that you can optimize your web pages to suit your own needs. You can "streamline" the code, cutting-out unecessary stuff to reduce page-loading times. You can also move important content to the top of a page, where it is more accessible and search-engine friendly, and then use CSS to place it wherever you want it to go.
One important thing though - you really need a thorough understanding of HTML and CSS to make a lot of difference when it comes to optimization. The performance gains are minimal; an optimized page may load in half the time, but that saving is only really sigificant in high-traffic sites.
Knowing how to handcode is really essential when it comes to dynamic websites, in my opinion. WYSIWYG tools have a tendency to mix up presentation and content with programming logic, which makes pages extremely difficult to debug and maintain.
In fairness to WYSIWYG editors, they have their advantages too. For example, it is possible to create pages very quickly. They can also function as a rudimentary content management system, making it possible for non-web savvy people to contribute to a page (although a proper CMS is a better way to go).
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