Why do women process oxygen faster than men?

It is incredibly hard to know for sure which evolutionary preasuress in our past led to specific taits we see today - in completly different enviroment - but my bet is on surviving childbirth in prehistoric conditions. Also note that women used to spend significant portion of their adult life pregnant, and so any form of resistance to exhaustion would be quite benefitial for them.

Some sources:

... increased aerobic fitness was associated with shorter labor in nulliparous women who started labor spontaneously.

https://obgyn.onlinelibrary.wiley.com/doi/full/10.1080/00016340903093583

... moderate-intensity exercise performed throughout pregnancy was associated with a reduction in the rate of cesarean, instrumental deliveries...

https://www.tandfonline.com/doi/abs/10.3109/14767058.2012.696165

There doesn't seem to be anything wrong with the paper, but as pointed out in the comments (and in the press release itself), the study was small, so any conclusions should probably be tentative. Adding a little more detail from the link:

For the study, which was very small, researchers recruited nine young males and 9 females, all roughly in their mid-20s. Females and males were of similar weights within their own genders. Everyone participated in the same exercise—walking on a treadmill—and scientists compared oxygen consumption and extraction in both genders during the workout. They found that the women were consistently more efficient than men, as they processed oxygen 30 percent faster.

Beltrame, Thomas, Rodrigo Villar, and Richard L. Hughson. “Sex Differences in the Oxygen Delivery, Extraction, and Uptake during Moderate-Walking Exercise Transition.” Applied Physiology, Nutrition, and Metabolism 42, no. 9 (2017): 994–1000.

A few more details from the paper itself:

• you have to be very careful about interpreting what "faster" means in this case. The paper says:

The greater maximal aerobic power [VO2max] of men compared to women is well recognized (Cureton et al. 1986).

For example, "good" VO2max for 20-29 year old males is 42.5-46.4 mL/kg/min: for 20-29 year old females it's 33.0-36.9 mL/kg/min. This means that at peak intensity, men can process oxygen faster than women.

• In contrast, the focus of this study is how fast women and men ramp up their O2 metabolism as they exercise.

Here's Figure 2 from the paper:

based on the figure and on table 1, the "mean response time" is about 50 seconds for women, 60 seconds for men.

• the other caution about this study (besides the small number of participants) is that the authors appear to have tested 32 different parameters of oxygen uptake metabolism, for both men and women; many researchers would recommend a multiple comparisons correction in this case, to account for the fact that it is more likely for some comparisons to appear significant by chance when making many comparisons.

Finally, it would be hard to be do much evolutionary speculation for the reasons behind these sex differences ... one might want to start by doing a comparative study, to find out if these differences are unique to humans or whether they also appear in our close relatives (chimps, gorillas, etc.)