1. Fixed barrels lend themselves to better accuracy. Some pistols have fixed barrels but all revolvers do, and they're truly affixed to the frames providing better and more consistent accuracy. There are extremely accurate pistols but taken as a class of weapons, revolvers are accurate.
2. Same trigger pull every time. Double-action-only pistols were created to cure the double action first shot/single action subsequent shots on traditional double action pistols. The revolver already offers that with a nice external hammer for single action shooting when desired.
3. Revolvers usually carry six rounds and the average police shooting involves less than four rounds with 60% misses. More might be better but six rounds have generally been sufficient for the last hundred years.
4. No magazines. The weakest part of a pistol is the magazine. Lose or damage a magazine and you may not be able to shoot even a single round depending on your particular pistol. Revolvers, on the other hand, need no loading device to operate.
5. Faster malfunction drills. The revolver has the world's fastest malfunction drill--pull the trigger. Of course, any handgun can break but most malfunctions relate to ammunition or brass and revolvers have a decided advantage when it comes to a bad round.
6. Tactical reload advantage. Magazines are quicker than speed loaders when the shooters are equal but pistols require all rounds to be removed whereas a revolver will allow spent brass to picked out of the cylinder when it is preferable to dumping the whole cylinder.
7. Speed loaders are much harder to break than magazines and a well trained revolver shooter can outpace a mediocre pistol shooter all day long. Training is the key.
8. A medium sized revolver allows a great variety of grip sizes to better fit its owner.
9. You can't cause a revolver to jam through "limp wristing" and it is extremely difficult to stop a revolver through close contact with clothing or solid objects. Slides can bite clothing and flesh or suffer function failures through contact with solid objects. Its rare for a modern pistol to fail but again, the revolver has the advantage.
10. If you already have a revolver the money you would spend buying a pistol is more than enough to pay for all the ammunition you need to develop fundamental skills. Learn and train, and you'll find yourself easily out-shooting the average pistol shooter.
11. Revolvers aren't ammo sensitive. Your six-gun won't malfunction because it doesn't like a bullet shape or a light load.
Revolvers are excellent weapons for self-defense and a pleasure for recreational shooting. If you're fortunate enough to own a service type revolver consider yourself well-armed.