Because its inherently appealing, close to what you wanted intuitively, and if you're only dealing with a single implementation of it, works fairly well.
You don't really get bit by its lack of a standard and extensibility until after you've bought in.
It's essentially designed by the opposite of a committee -- rather than including everything but the kitchen-sink, it contains support for almost no usecases except the one. Which is very appealing, when you only have the one usecase.
Well rst is better than markdown from day one. The only reason it became famous is thanks to wikimarkup.
So markdown needs to thank the popularity of Wikipedia for its success, as rst did not have any application like Wikipedia. But still rst is used widely enough with its killer Sphinx, readthedocs and now its kind of de-facto documentation writing markup in Python and many open source software world.
Because you can teach someone markdown in five minutes. And even if they don't know all the ins and outs, the basics are pretty foolproof (paragraphs, headings, bold and italic).
It's better than "designed by a committee" standards, but it lacks elegance or maybe craftsmanship.