Why isn't maximum current forced upon a circuit by a power source?
The "120 V 20 A" rating of a wall outlet means it will supply 120 V and up to 20 A.

What is implicit in this spec, and most power supply specs, is that the power supply is considered a voltage source.  That means it will try to keep its output voltage constant.  It only has this single degree of freedom.  The load then decides how much current to draw at that voltage.

For example, let's say your overall resistance (mostly due to relatively dry skin where the current enters and leaves your body) is 10 k&Omega;.  You grab the two wires from the 120 V outlet and (120 V)/(10 k&Omega;) = 12 mA will flow thru you.  That's way way less than 20 A, but still enough to kill you.

There are power supplies that regulate the current.  These are unusual, and will be clearly labeled as such.  A constant current supply might be labeled 1 A 50 V.  That means it will put out 1 A of current, but can only go up to 50 V.  If it would take more than 50 V to get 1 A of current thru the load, the output will sit at 50 V and the current will be below 1 A.