Beta males are passive people who do not stand up for what they believe in and probably struggle in social situations, have trouble establishing relationship and may have a tendency to be whiny and needy. This qualities do not paint a good picture of someone by either gender. However, in society, it is worse for a male to be a typical beta male as opposed to a female. On the other hand, it is frowned upon for women to be the alpha.
Due to stereotypical gender roles, the man is supposed to be tough and suave whereas the woman is supposed to be quiet and submissive. However, throughout the years, these roles have somewhat changed but they are still frowned upon today, but just not as much as in the past.