“Given all things are equal between applicants from each group”
This is an invalid assumption. The most obvious reason, for me, is that if a job ad specifies requirements for a position, men looking at the ad are more likely to apply for the position if they meet only some of the requirements, whereas women are likely to apply only if they meet all the requirements.
More subtle sources of differences are that the wording used in the job ad may make the position relatively more attractive to men or to women, or to people with certain personality traits, and that in order to increase diversity in applications, the ad may be advertised more to women. These may have subtle and unpredictable effects on the quality and quantity of male and female applicants.