Final answer:
Abraham fathered a child with his servant Hagar because Sarah, his wife, was unable to have children at the time. They decided to have a child through Hagar as a means to continue their lineage.
Step-by-step explanation:
Abraham fathered a child with his servant Hagar due to the circumstance of Sarah, his wife, being 90-years-old and still not having any children. In order to fulfill their desire to have a child, Sarah suggested that Abraham have a child with Hagar as a way to continue their lineage. This led to Hagar becoming pregnant and giving birth to Ishmael.