Geschwind, Behan and Galaburda have presented empirical research which indicates an association between left-handedness, immune disorders, and learning difficulties. Moreover, they have presented an hypothesis that purports to explain these associations, i.e. the 'testosterone hypothesis'. This article seeks to show that their hypothesis cannot explain: (a) which types and degrees of the conditions will appear, (b) why these conditions appear more often in males than in females, and (c) why these conditions seem to run in families. Moreover, this article attempts to show (d) that the hypothesis does not make clear the distinction between genetic and environmental factors, and that environmental factors are of greater importance. In addition, the hypothesis leads to great importance being given to purely random factors, because random factors alone determine whether or not a person with hemispherical symmetry will develop abnormal dominance Furthermore, this article argues that an hypothesis of this type should be based on a clear dividing line between latent and manifest symptoms, particularly when these are used to define research samples. Finally, (e) this article seeks to raise doubt as to the possible verification or falsification of the hypothesis by means of empirical studies.