Why are accident rates higher on smaller aircraft?
The amount of resources that go into commercial aviation are really amazing -- the amount of time, talent, money, and effort that have gone into making the airlines the safest mode of travel known to recorded history is really extraordinary, and the results reflect that.

Design

Aircraft are expensive, but a part of that expense is the extreme care that has been taken to make them highly reliable, with redundant systems and lots of advance warning systems when something is nearing the point of failure.  

Fifty years ago, aircraft were less reliable; the engineers have incorporated the lessons learned.  And, considering how much money an airliner make, airlines are generally willing to pay absolutely top dollar for the very safest design possible. 

Small aircraft have also benefited from this learning process, but as a matter of economics, they don't get quite as much redundancy or refinement.  While 99.999% might be "good enough" for the general aviation, the airlines can afford the (high) costs of adding more 9's onto the end of that number.

Maintenance

Again, the airlines can afford a maintenance process and inspection regime that would raise the cost of flying a light aircraft significantly.

Mechanics are trained to uniform standards and work in a carefully monitored environment where parts are exactly tracked and the aircraft have an incredibly detailed history of all that's been reported and fixed over their lifespan.  

Manufacturers like Boeing and Airbus can see millions of hours of data and spot trends that are developing to head off incipient problems before they become widespread. This, combined with the way that the aircraft are engineered, makes things really, really reliable.  

General aviation maintenance is good -- I'm not bashing that -- but airline maintenance, especially at the major airlines, is amazing.  That's not free, but the results are there.

Pilot experience and training

Light aircraft are often flown single-pilot, by a pilot who probably has under 2000 hours, and who may have flown 200 hours in the past year. 

On the other hand, airline pilots are typically hired with at least 1000 to 2000 flight hours, often more, and a captain at a major airline may well have 10,000 to 20,000 hours.  Added to that, the crew has probably flown between 400 to 800 hours in the last year, as well as getting multiple days of training -- both ground school and simulator -- as well as at least one if not two checkrides.  

Flying is their profession, not a hobby, and they spend time continuously studying the aircraft, its systems and checklists, the environment, and the regulations.  And, they're trained to work as a crew -- if one pilot is about to make a mistake, the other pilot is there to catch it and keep things on track. Not everybody flying light aircraft has these resources.

All of this is possible because, while it is all expensive, airlines can afford it.  

And the records speak for themselves -- one fatality in a commercial U.S. aircraft over the last several years -- which includes many millions of flights.  I don't think any other human activity -- including sleeping in your own bed at night -- can claim a similar safety record.

The relevant point isn't that light aircraft flying is "dangerous" compared to commercial aviation; it's plenty safe by normal comparisons.  It's just that airline flying is so incredibly safe, any other activity will look more risky in comparison.