I think I figured it out.
When you created the RAR file, you used the newer RAR5 file format that was released in 2013. Since I was trying to open it using an old version of PeaZip file archiver software from before 2013, PeaZip didn't recognize the newer format and assumed it was encrypted. I downloaded the newest version of PeaZip and now it works just fine.
If anyone else is having this same problem, try updating your archiver software.