Escape into the museum
Typically, symmetric knots are used either for decoration or for ease of untying under load (vis: 'square' or 'reef' knots; prized for running free when wet and under wind-load, but prone to self-unraveling if subjected to vibration or varying load, or loading other than on-the-bight. The Square knot is quite symmetrical but unsuited for climbing use per the foregoing reasoning.
Too, the square knot is often confused by novice tie-ers with 'granny' and 'thief' knots, both topologically related but treacherous for their own reasons. Easy-to-untie knots are also often vulnerable to 'upset' under load, (the square knot can be turned into a two-half-hitches or a clove-hitch without untieing it) and thus are considered 'weak'.
The stronger knots (bowline, sheet-bend, etc) tend to have a strong asymmetry to them, and self-lock under load. The 'best' ones can be untied easily with correct manipulation of parts of the knot that are not in the direct load path (the bowline is typically released by pushing one of the loops 90 degrees to it's preferred orientation) but it's virtually impossible to do so under load
Thanks for providing the explanation, why symmetric knots often are problematic, go to contributor MakerOfToys.