I know they're not used in military aircraft because it decreases the stealth factor, but why don't commercial plane manufacturers make variable sweep planes?
Variable geometry is not used in commercial aircraft design for the same reason that they initially became popular in the 1960s but have fallen out of favor in more recent times: any kind of aerodynamic performance gains associated with the design is not worth the additional weight increase, and subsequent decrease in payload, associated with variable sweep wings.
There have been attempts to do so in the past. The ill-fated Boeing 2707 SST was supposed to make use of swing wings but designers could not achieve their payload goals with the design. Usually more judicious application of aerodynamic principles during initial design is far more advantageous then beginning to design out right with a swing wing.
To enlarge upon Carlo's answer, variable sweep was intended to permit subsonic and supersonic flight. Since supersonic passenger flight is not viable from an economic standpoint, airplane designers do not have to accomodate it in their wing designs, and can support the low-speed flight regime with slats, leading edge droop, extensible flaps and drooping ailerons- which can all be incorporated into a fixed sweep wing which is otherwise optimized for subsonic cruise conditions.
The British designer Barnes Walls (famous for his bouncing bombs) developed a swing-wing airliner concept during the postwar period. It was a radical rethink which he regarded as no longer an aeroplane but instead he called it a wing controlled aerodyne. He flew a series of radio-controlled UAVs, Wild Goose being the first and Swallow the second.
They were aerodynamically exremely clean, Wild Goose being just a streamlined fuselage like a mini airship (he had also designed the R100) with two movable wings. There were no other control surfaces or tail plane. Swallow was a higher-speed development with its fuselage in the form of a delta-shaped lifting body and with swivelling engines on the wing tips.
Although he proved the aerodynamics, there were still a lot of technical unknowns. The cost and risk of developing such a brand new concept into his proposed non-stop England-Australia airliner was too much and funding ran dry in 1957.