Weeds are simply plants that suit their environment too well and succeed in ways we actually don't wish. Basically gardeners like plants that give them the most bang for their buck - but with a controlled bang. Weeds, and I've had many a battle, just don't fit the human idea of order and control. They are fighting for their lives like every other species on this planet.
Dandelions are the classic "arrggg" plant in the garden/yard. They are tenacious and prolific and we tend to miss the beauty in things that don't fit "our plan." They are astoundingly beautiful when you stop to look.