Cardio is not a faster way to lose weight for women (or men). The only way to lose weight is to eat fewer calories that you burn in your total daily energy expenditure. If one of the ways you achieve that deficit is with exercise (you can still lose weight by doing nothing and sitting on the sofa so long as you eat few enough calories) then you may as well lift weights rather than do cardio ( a nice mix of both would be better).
The main reason for this is that maximal strength is related to the number of muscle fibers pulling together, so when lifting on a calorific deficit your body will try to not burn muscle for energy as every muscle fiber is being employed to move weights, so instead will focus on fat.
If you lose weight on a cardio dominant exercise program the body will burn fat and muscle for energy as the fast twitch fibers primarily employed for lifting are not being used when running and so are as much a dead weight as the excess fat that is trying to be lost. This is why many cardio only people end up dissatisfied with their "goal weight" physiques because they lost as fat and muscle and still look quite soft - this can lead to excessive dieting and other such body image/eating issues.
Fundamentally (and barring any hormonal issues related to things such as the thyroid) losing weight is a calories in vs calories expended calculation. The type of weight you lose (muscle vs fat) is determined by the exercise that you do. Some studies have shown women who have low levels of fat and engage in a strength training protocol lose more fat than muscle compared to those who just stick to cardio.
The fact that women have low levels of testosterone compared to men is a big help as they literally can't get bulky and have very low amounts of visceral fat which is great for long-term health.
I don't think we are fundamentally disagreeing but I just want to highlight that women should lift just as much as men do.
