But Markdown doesn't compete with Word, really at all. There's no strong reason to frame them as opposites or to suggest that one can replace the other. Word is an editor, and Markdown is a spec. Word is wysiwyg, and Markdown is not. Word is built to handle large and complex documents with complex formatting and references, Markdown is (primarily) made for lightweight use to create simple web pages.
Word is simultaneously an horrific beast and a beautiful program, but the list of features Word has that Markdown doesn't support is probably 2-3 orders of magnitude larger than the list of features Markdown even has. Word can do everything Markdown can do, but not the other way around, even if you allow for arbitrary HTML (which is cheating).
I'm all for Markdown when it's appropriate, and while I try to avoid Word for simple text documents, there are absolutely times that it's called for. Definitely learn Markdown. And then use the right tool for the job.