The concept of "reasonableness" is surely subjective. What you might think to be a "reasonable" response from a person might be quite different to what I think is "reasonable." There needs to be very clear criteria to define what is meant by reasonableness.
If the law states "reasonable person" that would suggest that the criteria would be drawn from what a wide cross section of people would find to be reasonable.
If the law states "reasonable man," it suggests the criteria would only be drawn from what men believe to be reasonable.
Because men and women in general are socialised along gender lines in society, their concepts of "reasonableness" may differ.
And, unfortunately, there have been examples where the courts have used the definition of reasonableness as it applies to men, and not to people in general, when making decisions.
What springs to mind is the difference in murder and manslaughter. Men who have killed their partners have often been convicted by manslaughter because their counsel has successfully argued that they were provoked by something the woman did, they "just snapped" and killed them, so it wasn't premeditated.
However, until fairly recently, women who killed abusive partners after enduring often years of abuse were more often convicted of murder because it wasn't accepted that those years of abuse were sufficient enough for the "just snapped" defence to operate.