One of the factors you control for is job title. When you only compare people with the same title the wage gap shrinks a bit. For some reason people interpret this as "Great! Not a problem. Moving on." when it completely ignores that as a group women holding lower paying job titles is itself indicative of a problem -- career paths that are dominated by women are seen as less valuable and girls are socially pressured away from more lucrative careers (you know like software engineering where every woman in our field including myself can tell you stories of being the only girl in her class) by parents, academic advisors, the school and workplace culture the fields cultivate and pushed into "softer", "more nurturing", "more creative" career paths compared to boys.
Which it itself a problem for boys because boys who want to go into things like art, music, design, writing, fashion, social work, are mercilessly pressured away from it where girls are more likely to be encouraged. The patriarchy hurts everyone folks.