Why won’t my Jeep go into reverse? It will go into drive and move.

Sounds like something mechanical is going on. It really is impossible to say without inspecting it and performing the needed testing to verify all electronic components are functioning as they should be, not to mention transfer case operation. I'm sorry to say you'll have to have it checked. www.repairpal.com/repair-shops

i agree with davejm .this does not add-up .please have it check-out by a qualified professional