It's a big no-no in some design circles - it reeks of complacency, prestige, dullness. It is safe, unimaginative, old-fashioned, comfortably bourgeois. Symmetry. And yet...we like it.
In nature, symmetry is found on a small scale - individual organisms are often symmetrical (see the dragonfly above) and their symmetry is a vital factor in genetic success; many studies show that, in the animal kingdom, individuals with a greater degree of symmetry are more successful in passing on their genes - they are more appealing to potential sexual partners and so have a greater opportunity to breed. This is even true on a subliminal level in humans. However, increase the scale to anything above the level of the individual and symmetry in nature pretty much disappears - there are far too many factors at play in a woodland, lake or mountain range to permit such refinement, and the effects of weather, accident, uneven erosion all contribute to the geometrically chaotic result.
It is only in the human environment of architecture, planned settlements, gardens and managed landscapes that symmetry and order are evident on any large scale.
I think symmetry appeals to us, at least in the Western aesthetic, because it denotes control and order - it speaks to the deep instinct we all have to create order in our environment, and is a very visual demonstration of that ability. We keep the chaos of nature at bay, safely tamed and toothless, by channelling it into forms that simply do not exist in the wilderness. The creation of symmetry in our environment reassures us that we are safe from the wild wood, and its use as a device in our gardens stems from a specifically Western philosophy of the world, developed down the centuries and encompassing great thinkers from Aristotle to Descartes and beyond.
Of course the greater your ability to control, the greater the extent of your symmetrical interventions in the landscape. The favoured method for shahs, emperors, kings and caliphs to demonstrate their power has been to render vast tracts of land into managed landscapes, symmetrically ordered around their palaces and pavilions - the greater and more absolute the power, the more gigantic the scale of the works. At Versailles, for instance, the final extravagances of the French kings dominated the countryside for miles around the palace, with great avenues carved into the native forest to extend the sightlines from the terraces and windows of the buildings. The message was clear - the world revolved around the Sun King; he was the gravitational centre of the country and all lines led to his person.
These huge estates and landscapes send two messages - nature is subjugated, but so also are the people. All of these greatest gardens (settings to glorify, in most instances, powerful individuals) were created by the labour of numberless and nameless workers or slaves, pressed into service willingly or otherwise.
Very few of us now have the resources to command these forces, or indeed the acreage on which to deploy them, but we can all still enjoy the calm and sense of order that symmetrical spaces bestow. Symmetry works its effect on the smallest scale, and in these straitened times, with uncertainty at every corner, I would not be surprised to see a return to its wider use on a domestic scale. Sometimes the safe, the reassuring, the old-fashioned is what people crave, and if that comes at the price of a new pair of clipped yews either side of the front door then it seems little enough to pay.