Does synesthesia lack symmetry? Some synesthetes report seeing bright flashes when hearing a loud noise.  However, in the same person, bright flashes of light are not reported as being loud.  I've read of other examples like this; for instance, the number 1 may always be yellow, but yellow is not the number 1.

Has there been any research as to the neurological reasons why synesthesia is asymmetric?  Alternately, is my anecdotal assumption that it is asymmetric incorrect and there are actually frequent symmetric presentations of the condition?
Generally spoken, synesthesia is unidirectional. For example, grapheme–color synesthesia (i.e., letter–color and digit–color synesthesia) is the most prevalent type of synesthesia. The presentation of a
grapheme leads to an additional synesthetic color percept. Although
grapheme–color synesthetes are strongly influenced by the synesthetic color perception triggered by a specific grapheme, they usually do not report that a color triggers the perception of a specific grapheme.

However, while explicit synesthesia is unidirectional, there is evidence that it can be implicitly bidirectional. To show this phenomenon, clever experiments need to be devised. For example, the left-hand responses of digit-color synesthetes were faster for colors representing a small number,
whereas their right-hand responses were faster to colors representing large numbers. Hence, apparently there was an implicit association of the color with numbers.

Reference
Weiss et al., J Cognitive Neurosci (2008); 21(10): 2019–26