There are multiple possible explanations as to why they won't compete. One of them is incapability through biological inferiority, which I highly doubt is the case. Another is systematic bias. Another is really as simple as
not wanting to. Again, please read what is actually written, not what you want to answer to.
Frankly, this "discrimination towards women" may as well be turned around with one simple trick. Which of the two sexes is more likely to have their worth as partner be judged based on their ambition and achievements? Last time I checked, women are a lot more judgmental of their partner's ambition, earning capabilities, career, and similar traits than men are, frequently to the point of wanting a guy who is relatively "better" than themselves. You think that has no influence on competitiveness? When your worth as a romantic partner gets tied heavily to all those things, which can be found in a field emphasizing competitiveness, surely you can imagine men respond by being more competitive.
Now imagine your worth isn't as tied to this, you have all these men with a very clear incentive to compete keep trying to one-up another. It isn't a secret people give up easier when the challenge is too difficult compared to the reward, and assuming above, women clearly have less of a reward at the end of this.
Convenient excuses? Probably. Frankly, the entire "oppression" narrative is awfully convenient when put under the right angle. So instead of knee-jerking towards all this, let's stop this "trope" as well and address the problem for the multifaceted issue it truly is.
Edit: as replying to the below is no longer an option and apparently my "competition" claim is "unsubstantiated", it seems I have to point out the obvious. Women still largely go for men outearning them rather than equals, let alone lower.(https://onlinelibrary.wiley.com/doi/full/10.1111/jomf.12372)
Additionally, money helps men more than women when it comes to cushioning traits of lower value (https://www.sciencedirect.com/science/article/abs/pii/S10905...)
Though I guess one peer-reviewed study tracking diaries says more than entire countries filled with anecdotal data of women more willing to work part time even when not caring for kids.