Why does the color of light cause the color of the object to change

Because the color you see when you look at the object is
the color of the light that shined on it AND got reflected off
of it to your eye. 

So in order to see a color, that color has to be in the light that
shines on it, AND it has to be a color that bounces off of the
object and doesn't get absorbed by it.

A rose looks red because it doesn't absorb red light, so when
red light shines on it, the red light bounces off of it into your eye. 
The rose absorbs all other colors.  If there's NO red in the light
that shines on the rose, then the rose will look black !