Where do you get that from? I've found it a bit difficult to get data about single parent households, rather than unmarried parent households, as those are not necessarily the same thing. However, from the little I have seen, it is not true that half of white homes do not have a father present.
For example, according to this
Children in single-parent families by race | KIDS COUNT Data Center , 24% of non-Hispanic white children live in a single-parent family, if single-parent is defined as "Children under age 18 who live with their own single parent either in a family or subfamily. In this definition, single-parent families may include cohabiting couples and do not include children living with married stepparents. Children who live in group quarters (for example, institutions, dormitories, or group homes) are not included in this calculation."
Or there is this
Single-Parent Families, by Race/Ethnicity | Data and Trends in Quality of Life for Greater Rochester Region , which while it is about New York, also gives statistics for the country as a whole. This page lists the single-parent family percentage for whites at 33%.
I expect it is a lot easier to get statistics for married vs unmarried mothers than it is for whether a child has a single parent in the home or more than one, as different people might define what constitutes a parent differently. Is it only when someone marries? Can a long term but unmarried significant other be considered a parent? What about married couples who do not live together, does that skew the stats? Then there is the question about whether a child in a single-parent home is still getting enough support from the parent they do not live with; just because a single parent is the custodial parent does not mean the other parent cannot be a positive influence on a child's life.
There are a lot of factors involved in this discussion. I am curious where you get the data indicating that half of white homes have no father present, though.