No, she doesn’t. The children should be with the one who can have a “better development”. And this will depend on the specific case, evaluating:
1. Who has more time to take care of the children. Either by the agreed family role, or by the mood of each parent to devote time to the children.
2. The personality of each one. There will be parents more affectionate than others, willing to take care of the children’s homework, ask them about their friendships, etc.
3. The habits of the parents. Of course, a parent with harmful addictions (alcohol, drugs, etc.) would not be ideal. At the other pole we can put a parent with healthy habits such as balanced eating, exercise, and other activities that could radiate a good example to the children.
Any other fact that is considered relevant for making such an important decision.
The gender issue could only be relevant taking into consideration very particular situations of the specific case. As it might be if you are analyzing the case of a child who is still breast feeding. In such cases, unless the mother lacks suitability due to other factors (vices, mental disorders, etc.), she will be the ideal one to take care of the child, due to the ease of giving breast milk.
