Why can't most jets safely use reverse thrust while airborne?
The problems are two-fold:


The airspeed is much higher in flight than when landing, so the thrust reverser doors would have to be much stronger, and therefore heavier to withstand the additional forces, along with the relative wind making them harder to close. 
What happens when it gets stuck in the deployed position?  Now you have to shut down a perfectly good engine and have additional drag on the airplane while in flight.
(Bonus) It isn't really needed on most airplanes with spoilers, flaps, etc. that accomplish the same thing.