Not to knock on Adobe, but until they figure out that this function is needed (this thread has been around for 4 years, do they read these things), you can use this:
It does exactly what you are asking for, and it is free. Once it is open, select "alternate mix".
There are many other functions too.
Adobe, if you are reading this, please compile your programs for Linux to please.
Took me about an hour of googling and trying different options. Honestly I don't really know what a java script is so the best option for me was a program that could do this. Just use alternate mix like he said. Cheers
Thank you LarrySmith1000
Couldn't get scripts to work with new version but this worked for Adobe DC.
There has only been a minor update to Acrobat DC.
Make sure you are placing the scripts in the appropriate folder for your version of Acrobat/Reader.
Yes, Ideasmith gave the only true usable method, the other are talking greek. Well, the is a software called pdfsam it is free for mac or windows and it has a very simple option called "alternate mix", you do not have to split your file into single pages, you just take the two files and say: I want you to mix them, this is the odd and that is the even. Simple as apple pie. It astounds me why acrobat does not feature such a solution.
Create Odd folder Save As (Export) Book.png. Create Even folder Save As (Export) Book.png. Copy the contents of the Odd folder into the Even folder. Copy, but keep both files. You will have Book_Page_001.png and Book_Page_001 (2).png (the Odd counterpart). Combine all the files in the directory into a single PDF and BAM there you have it.