You just have to come up with an example that shows this can happen.

Here is an alternative formulation that you may find useful: Suppose you have a graph with 5 nodes, in which every node is connected to every other node. See if you can find a way to color the arcs with two colors (red and blue, say) so that there is no triangle (three nodes and their connecting arcs) with all its arcs the same color.

The 5 nodes correspond to the 5 people and the colors correspond to friendship or its opposite.