From Sheldon Brown, who sings the praises of fixed gears:
"Fixed gear dangers:
I should warn you that there are three dangers related to fixed-gear bicycles that are not a problem with freewheel bicycles. Used and maintained properly, fixed gear bicycles can be as safe as any, but you should be aware of the three danger areas:
Pedal Strike
It is never a good thing to strike your pedal on the ground while cornering tightly. On a freewheel bike, you can coast though the corners with your pedals horizontal, thus avoiding any chance of striking. On a fixed-gear machine, you don't have this option.
If you do bang a pedal on a fixed gear, the pedal can lift the rear wheel off the road, and down you will go. This has never happened to me, but it is something to bear in mind.
How much of a problem this is will depend on your bottom bracket height, crank length, and the design of your pedals.
Most of my fixed-gear bikes have 165 mm cranks,which give a bit more ground clearance than the 170 mm's usually used on road bikes. I also make a point of using pedals that don't stick out too far.
Derailment and Wheel Lock
Throwing a chain on a freewheel bike is no big deal, but it can be very dangerous on with a fixed gear. If the chain comes off of the chainwheel, it can get hung up or even loop around the rear sprocket, and can cause the wheel to lock up. If this happens while you are leaned over in a turn, you will almost certainly crash.
This is prevented by making sure that your chainline is straight, and that your chain is adequately tight.
Catching Fingers, Trousers, Shoelaces
The other danger of fixed-gear bicycles is at its greatest when the bike is in a repair stand. If you hand-pedal it and then accidentally have a finger an article of clothing come into contact with the chain or a sprocket, the momentum of the wheel will keep the drive train rolling. You can lose a finger that way."
I would argue that because geared or single speed bikes don't have these problems, those bikes are easier for a beginner to ride, and thus, more suitable for beginners.