Given that GitHub provides GUI apps for both Mac and Windows, what are the benefits of learning to use git from the command line? 

Currently I'm using their mac app to update my repositories, and so far it seems to cover my needs. What might I be missing out on?

I think this question is just a special case of "Why should I learn any CLI for which a GUI alternative exist?". I suspect the latter question is about as old as GUIs, and I assume there were many attempts to answer it over the years. 
I could try to bumble my way through my own answer to this question, but Neal Stephenson articulated what I agree with as the 'ultimate answer' more than ten years ago in his remarkable essay In the Beginning... Was the Command Line.

While the essay touches on many aspects of computing, and while even Stephenson himself thinks that a lot of it is now obsolete, the essay explains in what ways CLIs are better GUIs in an extremely compelling manner that literally changed my life. It's a long read (~40 pages), but I can't recommend it enough to anyone who asks questions like you asked here.

Finally, though I'd answer any CLI vs GUI sort of question in similar vein, I think my answer holds especially true to your specific question since of all computer things you chose to ask about git. git is arguably the latest tool in a not-so-long list of computer tools that are truly worthy of the hole-hawg metaphor as described in Stephenson's essay. git, like several other Unix-ish things, is a reason to know CLIs all in itself. Sometimes in spite of its erratic 'porcelain'; sometimes because of it.

So yes, you can definitely be productive with github's GUI, either for OSX or even just on their website. Yes, it's actually quite sleek, I use the features of the site often. But no, you will never have that Godly feeling as your right pinky hangs above an insane git filter-branch command for an aeon or two. If I had to keep just one thing from my experience with computing -  the mental challenges, the close friendships formed in a datcenter at 2AM, the infinite ladder of competence to climb, touching users' lives and reigning over PBs of precious data, the cushy jobs and comfortable life - keep just one thing - it'd be that Godly feeling.
