but here are my general observations.
Male protagonists are permitted to go on violent sprees to avenge the harms inflicted on female loved ones, but not on themselves. They often may have endured horrible tortures personally, but their violent vendettas are rooted in harms to women who they must protect.
Villains, however, frequently base their vendettas on harms to themselves, rather than loved ones. Silva in Skyfall, or Lex Luthor in some Superman versions, are examples. It is a sign of vanity and weakness if one goes on a vendetta to avenge harms done to one's own person.
Unless you are a woman, because female protagonists - unlike male protagonists - are permitted to avenge themselves. Which I take to be a subtle suggestion that women are expected to be vainer and more self-centered than men.
Generally, when heroes - male or female - avenge others, those others are female. Both women and men may avenge mothers, female lovers, daughters, female friends, sisters - but not men. Presumably, this is because women are viewed as uniquely vulnerable and helpless; men are expected to care for themselves, and so harms done to them, while tragic, are not worthy of vengeance by heroes (though they might be by villains).
There are exceptions - I can think of several off the top of my head. Khan avenged his wife; Maggie Q's Nikita avenged her male fiance. Emily Thorne/Amanda Clarke is sort of avenging her father, although she's also largely avenging herself so I'm not sure how much that counts. Nonetheless, I believe these are decently accurate general rules.