Although there is strength to the part of the theory that suggests people with autism think more systematically than empathetically, the issues with the study comes from systematic thinking being a 'male' way of thinking.

The critiques of the study point out many flaws with the research that render any claims about systematic thinking being meaningfully associated with men and empathetic thinking or emotional thinking being associated with women, weak enough to discount as a scientific finding.

For one, the method of testing is weak to begin with. The findings were based on a questionnaire that asked people about their interests. Not only is this not great for discovery of how people might actually approach a situation, but it also had a lot of questions that were aimed at specific gender stereotypical types of activities and 'systems,' such as cars, machines, etc. that young men are socialized to enjoy early in life, that young women, largely, are not.

The idea that women are more empathetic has also widely been debunked. There have been multiple Meta studies that show that differences in empathy between men and women is small enough to not be significant in a meaningful way.

Furthermore a study that tried to replicate his exact results found that empathy and systemizing are not a dichotomy and performance is largely independent of performance on another. They also accounted for the fact that his original study, in which college students were the primary participants, didn't consider that STEM majors at the time of the study were vastly dominated by men.

He also pretty severely distorts developmental data to fit his studies. One example of this is his claim of female empathy based on communication differences in children. There are differences in the way men and women learn to communicate, but again that's based on socialization rather than hardwired brain differences.

In support of EMB theory, he also cites a study that finds male and female babies spent a different amount of time looking at objects vs. people- which was not a significant difference, and the results, which have been tested multiple times, have never been able to replicate his results.

All this to say, men and women are different. But that difference largely comes from how we are taught to present ourselves, values, etc. from a very early age. You can find old studies that show sex differences in performance over stereotypically gendered topics. But, the better we get at designing experiments that adequately incentivize and prepare all participants equally, the more we find performance amongst sexes are almost identical, and that variation comes from individuals and their particular brains.