(picture from [1], but the color added by the author.)
You said “once you are on a green circle”, but what happens if I’m not.
O.K. Let’s assume you have an antenna with its impedance Z=25+j50 [ohm], which is z=0.5+j1 on the Smith Chart (the red dot).
So we start from the point in red, and somehow must go to somewhere on the green circle. How can we do that?
Well, there are two ways…