I found different forms of the quote on the internet, and mostly without sources. Which one is the original Batman quote?
Remember to always be yourself. Unless you can be Batman. Then always be Batman.
And who is the author?
It's probably just a viral internet meme that wasn't started by anyone well-known. Here is a list of dated twitter links to various early appearances of the quote, or ones that may have inspired it. You can see there are some early examples which don't quite match the finished quote but sound fairly similar, like this one from August 2009:
Life lesson; You can't go wrong when you be yourself, if you go wrong being yourself, don't be yourself, fuck it. Be Batman, or someone else
Or this one from November 2009:
If you aren’t going to be yourself, be Batman.
The earliest one the site found that matches the current one pretty well is this one from May 2011:
The most important thing in life is to be yourself. Unless you can be Batman instead. Then be Batman. Always be Batman.
I don't think there WAS an original Batman quote. There have been motivational posters about being yourself for years.
I remember several years before the Batman quotes became popular: "Always be yourself, unless you can be a unicorn, then be a unicorn!" I always responded: "Being a unicorn sucks, no one wants to play leapfrog with you."
It was after 4-5 other variations of these that I remember seeing ANY Batman ones.
So... IMHO, it started as an online joke, and has evolved the same way, online.