Or something resembling evolutionary psychology, my closest experience to evolutionary psychology are genetic algorithms. Before starting, please bear in mind that the post is purely speculative (for fun), do not take it too seriously, and finding evolutionary-psychological reasons for behaviors does not make them more acceptable. More importantly, there are probably countless women that have already explained this better than I will do.
Since homo sapiens sapiens exist, gender roles have been clearly differentiated for most of the time, they are potentially both consequence and cause of any possible sexual dimorphism, and mansplaining may be caused by the sexual dimorphism. In the remaining paragraphs we are going to explore how this could be possible, using maths, no numbers, and the 346 words left for a total of 500.
The scalability of reproductive capabilities is greater for men than for women, especially in the past. When choosing one or several partners, men tend to blacklist (or not be any selective) while women have a stronger tendency to whitelist. Reproductive cost is greater for women, and therefore their risk aversion. This difference in risk aversion and preference between women and men is the only point needed for the explanation.
Risk aversion and preference are statistically different in women and men, in part due to the differences in hormone levels, and their impact on risk preference. Even evolution itself has “decided” to place higher risks on men, with the chromosome Y being a fragment of chromosome X, men have only one copy of some genes when women have two, leading to greater variability (potentially also for some good things) and risks (e.g. color blindness). As a society, it running some risks on males makes sense, one can generate the entire offspring of a populous next generation, which is more difficult for females. The greater male variability suggest additional risk aversion to females.
“Better to remain silent and be thought a fool than to speak and to remove all doubt”
As a consequence of all the previous, there is a clear incentive (and risk preference) for men to try luck at explaining and signaling a greater status, to make into the white list, into which they are not a priori. Similarly, there is a greater incentive at remaining quiet and being cautious (and risk aversion) for women, as they are not in any black list a priori. Do not get confused, playing the status game is not a strategy for reproduction (especially after vasectomy) as much as a consequence of having been selected in it and a habit or inclination.
An additional element to consider is the competitive and collaborative natures of men and women respectively, which certainly interacts with all of the above, but that is something to analyse in other occasion, this is enough SciFi, insulting true science (and perhaps women and men) for today.