Even for traits with the same average, there are often big differences in the statistical spread between men and women.
There are a lot of traits, both physical and mental, where men tend to be either really crap, or really good (statistically speaking), compared to women who have that trait clustered more in the middle of the spectrum. If you take a sample based on one of these traits of "middle or better" you get statistically more women than men (which would explain more female undergraduates, as a fair thing), but if you take a sample of "only the best", or "only the worst" it skews more and more towards males as you take smaller samples, explaining more men at post-graduate levels, which are more competitive. Since men tend to have more concentration at both the top and bottom of such traits, if you say it's all due to social bias, what exactly is happening? the system is both biased for and against males at the same time?
Similarly for traits that require great strength. If you need strength X to do job Y, the more competitive it is, assuming strength translates to productivity, you're going to find way more men than women. The "top 5%" of strength is going to have a larger percentage of men than e.g. the "top 10%", and so forth. Explaining why so many jobs like construction, mining, furniture removal, are heavily male-dominated. You just can't be strong enough to do these jobs.
I'll wager that there are many jobs where the "optimal" strength is actually WAY higher than the actual maximum human strength. The odds of a task having an optimal strength exactly close to the human maximum is close to zero - it's really unlikely. Think about a job: "would Superman be better at this job than a strong human?". If, so then, strength is highly relevant to performance for that job, and you can't have enough.