Why are most cranks old men?
In order to assess this claim, it is important to first bear in mind that classification as a “crank” theory actually requires a reasonably high level of technical development.  For example, in the linked article on trisection of an angle, it actually takes quite a bit of skill and work even to come up with a plausible-sounding false theory of how to do it.  There are almost certainly millions of adolescents in geometry classes around the world who would think that you can trisect an angle using straightedge and compass, and are willing to give it a go.  You would probably find thousands who think they have figured out how to do it.  The reason we don't class these kids as “cranks” is not because they are any smarter than the “cranks”, but just because they lack the time and technical skill to put forward a plausible-looking method, backed up by technical argumentation.  Even if they did, you wouldn’t tend to call an adolescent a “crank”, since the expectation of knowledge is lower.

Secondly, one should consider the likely preconditions for spending a large amount of time trying to prove something that professionals in the discipline assert to be false.  This will generally occur only if: (1) the person is of the view that these authority figures are fallible, and there is some reasonable prospect of success; or (2) the person gets direct enjoyment from the challenge, regardless of its impossibility.  Therefore, a “crank” is more likely to emerge among people who are either sceptical of institutional and professional authorities, or among people who get direct enjoyment from playing with technical problems.  Having then found a “solution” that appears plausible to them, what are they supposed to do?  Keep it to themselves?

Thus, assuming that your hypothesis is true (i.e., that most “cranks” are indeed older men), I would posit that the most likely explanations are probably a combination of the following factors:


There are far more men than women in technical professions that give them the requisite skill to develop a “crank” argument (ergo more men than women);
There is strong evidence that men score lower than women on the personality trait of “agreeableness”, and they are also much more interested in things in the people–things dichotomy.  There is some psychological evidence that men are more sceptical/resistant to institutional authority.  They are therefore much more likely to satisfy the preconditions for gaining utility from working on a problem that is asserted to be impossible by professional authorities (ergo more men than women);
In order to develop a theory in sufficient technical detail to be considered a “crank”, one needs a substantial amount of technical training, e.g., in engineering, mathematics, physics, etc., and there are more men and older people with this technical training (ergo more men and more older people);
In order to develop a theory in sufficient technical detail to be considered a “crank”, one needs a substantial amount of time, such as would be available in retirement (ergo more older people);
Even under equivalent circumstances, an older person is more likely to be classified as a “crank” than a younger person, due to the fact that certain younger people (particularly children, adolescents, and young adults) are not expected to have a high level of technical knowledge, and are generally excused for making assertions that are belied by expert knowledge (ergo more older people);
The context for discussion of “cranks” often tends to be technical disciplines like mathematics, engineering, physics, etc., which are heavily dominated by men.  There are many other fields of interest dominated by women, where silly ideas are ubiquitous, but these tend not to be raised as examples of “cranks” in these kinds of technical discussions.  For example, for every male “crank” in the field of mathematics, there are probably a hundred woman who believe in crystal healing or tarot cards, or some other scientifically baseless idea in a field that is more popular with women (ergo more men than women);


Incidentally, these are exactly the same reasons why the vast majority of correct technical methods in the fields of mathematics, engineering, physics, etc., are developed by men, with a reasonable representation of older men – for every few “cranks” that put forward asserted proofs of false theories, we get an innovator who breaks new ground with a correct theory that extends existing knowledge.  In any case, these are just hypotheses, but they seem pretty plausible to me, and I am not aware of any literature that attempts to study this problem.  Personally, I find it unlikely that a gender imbalance is due to women “having too much sense”.  Both sexes can lay claim to a great many people with very little good sense, and in my observation, various women spend absurdly large amounts of time on activities that are no less ill-advised than trying to prove/disprove difficult/impossible technical theories.