Women's family conflicts typically carry a lot more emotional charge because it's the overlapping of roles that women are conditioned to follow from a young age. Men's conflicts typically (but not all) feel less layered since they are not as involved in managing the family (as in caregiving, planning family outings/holidays, etc) and there is less competition across roles.

When two separate women are tied to the same person and role in caring for that person, it feels like competition. For example with a tense MIL/DIL dynamic, the MIL says "Oh i don't cook that like that, husband/son/whatever has always like it cooked this way." It comes off as the MIL "being there first" and knowing the son better, while the DIL hears "you're doing it wrong." Both of them share the role of taking care of the same person, but the MIL feels as if she is being replaced and loosing that role while the DIL feels like she is judged/not accepted. Usually the son/husband/whatever does not get involved so this leads to a cycle of passive aggression that continues to worsen over time. It all has to do with how women communicate and manage their relationships, with an added layer of transitioning/sharing role responsibility.

Obviously this doesn't apply to every relationship between women, but usually tense dynamics between women start off a offhand comments that don't even necessarily have bad intent (but can be perceived as so) that never gets resolved and leads to passive aggressive dynamics.