Don't play on the point of symmetry
Like any other proverb, there are exceptions to the proverb play on the point of symmetry.
The symmetric problems page contains some problems where this proverb does not apply.
Example 1
The solution is just beside the symmetric point. Of course, being a symmetric position, can also play at a.
If blocks, then
is the vital point. After
, a and b are miai, so White dies in a straight three dead shape.
Example 2
The trumpet connection, which is the symmetrical move, is normally not recommended.
Surely this isn't white's best response though, he didn't even try to resist the second peep. ~srn347
Any solid connection is recommended, because it leaves Black with at most one peeping point.