Although we're always looking for a different angle in photography, symmetry can also be pleasing to the eye, and is actually a necessity quite often. Can you imagine if people had their nose placed on the right side of their face, or one ear on the back of their head and another on the left ? Just wouldn't look right, would it.
Symmetry can be found in man-made structures as well as in nature. I found symmetry in both today.
(18-55mm f4.5 1/50 sec ISO200)
Then there was this photo that looked to me like a sound wave or a seismic graph:
(18-55mm f5.6 1/8 sec ISO200)
But that's only because I rotated it 90 degrees. Here's what the original looked like: