"To favor that parent" means to give preferential treatment or show a preference for one parent over the other, often in terms of support, affection, or choosing sides in a conflict or disagreement. Full definition
However, the best interests standards do favor the parent who typically cared for the children during the marriage, and this is often the mother. (info.legalzoom.com)
It's important to communicate with your spouse and allow the «not as favored parent» some alone time with the baby. (dudestodads.com)
The court favors parenting time to those parents who do not have custody of the children. (parentherald.com)