Why does Stack Exchange use Markdown? I think HTML could be fine as well. Does Markdown have more advantages over HTML?
These are the reasons I can think of:
It's easy: Using markdown doesn't require any technical knowledge whatsoever. The syntax is so simple and it's very easy for people with any level of technical skill.
It's fast: It speeds up the workflow significantly. You don't have to bother about getting the HTML markup right. Markdown does it for you.
It's clean: Markdown creates perfectly formed HTML for you. You don't have to worry about improperly nested tags, unclosed tags or anything. Markdown takes care of it.
It's suitable for all workflows: Stack Overflow is not the only site that uses Markdown. AFAIK, all the Stack Exchange sites use Markdown for formatting. As Oded said in the comments below the question, you can't expect the users of pets.se or gaming.se to know HTML. Markdown is not as hard to learn. If you can write a simple smiley, you can use Markdown. It's that simple!
The first and foremost reason to use markdown instead of plain HTML may very well be security.
Just think what code-injection nightmare embedded
<script \> tags could be.
It's probably easier to build a simple markdown language than to sanitize whatever HTML code users will throw at you.