How is the statement,'A plague on both your houses' relate to Romeo and Juliet?

The main idea of the quote is to bring out the idea that
no one really wins in an intense rivalry. Rather than awarding one side "the winner" in
a competition of such intense magnitude, the third path of seeing both sides as losing
is the underlying idea of the quote.  The idea of a "plague upon both houses" reflects
how each side is as fundamentally bad as the other.  It is here where I think that the
ending to the drama supports the idea of a "plague upon both houses."  This is seen in
the Prince's speech at the end of Act V. Both houses end up bearing striking similarity
to one another of the narrative.  Each has lost a child to suicide.  Each struggles to
make meaning of the loss.  Each house cannot fathom why their beloved felt compelled to
take their life.  The "plague" on both houses is the fundamental struggle of
understanding how their hatred and enmity could lead to the death of a beloved child. 
It is here where the quote is felt the strongest.  The Prince brings this out in
suggesting both Capulet and Montague are to blame for their child's death. It is at this
moment where the quote's sentiment is felt the strongest.