If you generally press overhead with back support, I'd imagine it could very well result from you not being accustomed to stabalizing the bar overhead - particularly the eccentric/negative portion of the rep.
I really encourage people to press standing doing either a military or push press. It's much more stimulative to the entire body's musculature, provides you with significantly more functional strength, and increases have a major carryover into other movements. If you put 50lbs on your best set of 5 in the push press, you can bet your benches are going to move up fairly easily.
Over the past 20 years, overhead work has really lost it's emphasis and I'm of the opinion that the increase in shoulder injuries is not a coincidence but more of a causality from lack of focus on these very valuable lifts that provide a lot of strength and stability to the entire shoulder region and associated musculature. Note that while the bench press has retained it's devotees (maybe even increased with the popularity of PL), the number of benchers with strict bent rows (when executed properly the same plane as the bench) in the 80%+ range of their best raw bench and solid overhead strength has decreased dramatically. Hence, lack of symetrical development, yielding instability, increasing incidence of injury. My thoughts anyway.