A father does not have fewer rights than a mother just by virtue of being male. It's something that fathers must remember to protect themselves. Biases in court are not only unfair but also illegal.
It is not true that women are more likely to have custody of their children as a result of a bias in court. In fact, fathers have the same rights in seeking custody as mothers. However, there are some factors that lend to women obtaining more custody over men that may come up in your case. These factors include things such as:
- A mother's time spent at home raising your child
- The nature of their relationship (mothers who stay at home with children may have a more significant bond)
- Having more time to raise a child due to a flexible work schedule or maternity leave
...and so on. There are factors that can lead a court to approve custody that is in favor of the mother, but that doesn't mean it always happens or that it's based in bias. There are some situations, however, that are clearly biased. For instance, if you are a stay-at-home father and spent most of your time raising your children, it would be unusual to see your wife end up with primary custody. It would also be a bias if anyone suggested that the mother would be better at caring for the children or that women are better parents.
Your attorney's job is to help you make the best case for custody and to help you avoid bias in court. By being aware of the actions of those around you and the court's tendencies, it's easier to get the custody arrangements you want.