Men have a noticeably higher percentage of muscle than women, and a greater body mass, overall this averages out to nearly double the protein requirement.

Meat is not the lone source of protein, however, loosely speaking, since women use a larger percent of their caloric intake to maintain body temperature, they do not require as high a ratio of protein. Heat loss is a matte rof surface area, women have nearly the same surface areas as males but nowhere near the net weight. For this reason, a woman can gain sufficient protein without eating meat, many vegetables are 20-25% protein by calorie after all, ditto milk. She, weighing say 50 kg, low 100's lbs etc, needs only 50 or so grams of protein, 200 calories, easily obtained on almost any diet, as even a diet of low protein bread or pasta will suffice. A male who eats that way, to obtain sufficient protein, will grow fat. He need not eat meat, but his diet will require heavy tuning in preference of high-protein veg and grain. Any low or zero protein foods will weight the total intake badly against him, whereas excess protein in one's diet has no negative effect (barring truly excessive examples). As my mother, a vegetarian, often points out, most women have little need to eat meat at all, growing up a vegetarian, it was necessary to alter my diet in my teen years, and I put on much fat until I began eating meat regularly.

Mammals use much and often the majority of their calories to stay warm, but typically need around (very rough value) about a gram of protein per day per pound of muscle to maintain that muscle. At the loose general average of 42% muscle for men, they can no longer expect any diet to provide sufficient protein to keep that muscle. As mentioned, your average female (muscle mass in low 30s) is using a larger portion of her calories too maintain body temp, again, surface area is the only noteworthy factor in heat loss and women parallel men in surface area far closer than in body mass. That effect should not be minimized, because most women in good shape must spend more calories staying warm then men do, pound for pound, and because men contain more muscle than women, pound for pound, they require a significantly larger percentage of their diet be protein, which meat evens out, allowing for instance, a normal male sharing meals with a normal but vegetarian female, could eat the exact same meal with the addition of a serving of meat, and both would be fine.