That is strange. I would consider a visit to the Adobe forums as well. I think there is a better chance of getting an answer there. They are quite helpful.
There was something with an older version of PhotoShop Elements that was already the required 64-bit version, but PSE would shut down without warning as soon as you clicked or used a key command. I found that I had to turn on Full Disk Access for PSE in System Preferences> Security & Privacy > Privacy tab.

Neither Adobe or Apple had any info on this so i had to virtually stumble into the answer. PSE 12 now works without issue.
I suggest leaving this question open here in case someone else has a thought on what's happening.