Safety of GA flying

Many times I am reading a magazine related to flying and some aviation
related newsgroups and there are a fairly large number of people that
are dying, crashing, etc.
Even the post a bit below about OSH show, etc.

Since I would like to learn to fly I have one question:

Airplane is considered to be the most safe mode of transportation.
Looking at the airliners and their operation where they fly 24/7 all
over the world, seldom some crash happens. What is the root cause and
problem in general aviation regarding safety, crashing, etc? Shouldn't
the standards be the same and are they the same in terms of flying,
rules and equipment. Basically, I wonder, what is going on and most
importantly what to do to correct it? And why it hasn't been done yet?

Thanks