This is not true.
Pick a random real number from interval [0,100]. What is the probability that picked number is not 7? Clearly 100%. Does it follow, that picking 7 is impossible or that number 7 does not exists? Clearly not.
Divide unit circle into 6 equal arcs. Paint those arc blue and green alternately (so that six end points of the arcs are painted alternately too).
You have an "impossible" blue-green circle.
In fact you can take just one arc (1/6 of circle) and paint it any way you want. Then for each point P of the arc take a regular hexagon H inscribed in the unit circle such that P is a vertex of H, and paint the other 5 vertices of H alternately (regarding color of P). Again you have an impossible blue-green circle.