These articles Here and Here highlight different modes of arguing. MRAs are modernists; feminists are postmodernists.
Here are some of the characteristics of each:
Modern discourse
• "personal detachment from the issues under discussion," the separation of participants' personal identities from subjects of inquiry and topics of debate;
• values on "confidence, originality, agonism, independence of thought, creativity, assertiveness, the mastery of one’s feelings, a thick skin and high tolerance for your own and others’ discomfort";
• suited to a heterotopic space like a university class, scholarly journal, or session of a learned society conference, a place apart much like a playing field for sports events, where competitors engage in ritual combat before returning with a handshake to the realm of friendly, personal interaction;
• illustrated by debate in the British House of Commons;
• epitomized by the debates a century ago between socialist G. B. Shaw and distributist G. K. Chesterton;
• playfulness is legitimate: one can play devil’s advocate, speak tongue in cheek, overstate and use hyperbole, the object being not to capture the truth in a single, balanced monologue, but to expose the strengths and weaknesses of various positions;
• "scathing satire and sharp criticism" are also legitimate;
• the best ideas are thought to emerge from mutual, merciless probing and attacking of arguments, with resultant exposure of blindspots in vision, cracks in theories, inconsistencies in logic;
• participants are forced again and again to return to the drawing board and produce better arguments;
• the truth is understood not to be located in any single voice, but to emerge from the conversation as a whole.
Postmodern discourse
• "persons and positions are ordinarily closely related," with little insistence on keeping personal identity separate from the questions or issues under discussion;
• "sensitivity, inclusivity, and inoffensiveness are key values";
• priority on "cooperation, collaboration, quietness, sedentariness, empathy, equality, non-competitiveness, conformity, a communal focus";
• "seems lacking in rationality and ideological challenge," in the eyes of proponents of modern discourse;
• tends to perceive the satire and criticism of modern discourse as "vicious and personal attack, driven by a hateful animus";
• is oriented to " the standard measures of grades, tests, and a closely defined curriculum";
• lacking "means by which to negotiate or accommodate such intractable differences within its mode of conversation," it will "typically resort to the most fiercely antagonistic, demonizing, and personal attacks upon the opposition";
• "will typically try, not to answer opponents with better arguments, but to silence them completely as ‘hateful’, ‘intolerant’, ‘bigoted’, ‘misogynistic’, ‘homophobic’, etc.";
• has a more feminine flavour, as opposed to the more masculine flavour of modern discourse;
• results in "stale monologues" and contexts that "seldom produce strong thought, but rather tend to become echo chambers."
TL;DR: Modern discourse is a method of evaluating the truth. Postmodern discourse is a method to enforce conformity in the in-group and to separate the in-group from the out-group.