simulation - KCL vs KVL in circuit analysis

I'm making a simplified version of SPICE to teach basic electronics to high school students (This is for a high school independent study).

Why does SPICE analyze circuits using Kirchhoff's current law instead of Kirchhoff's voltage law? Usually you have a voltage source to start with instead of a current source, and it is easier and more efficient to analyze a circuit using voltage instead of current.

Using voltage to analyze circuit: (See best answer) Circuit Simulation

Using current to analyze circuit: http://en.wikipedia.org/wiki/Nodal_analysis

Thanks!