Jesus makes the analogy so that people will understand that God cares for us as a parent cares for a child. Some might say that he knew what He was doing when he opted for using “Father” as opposed to “Mother.”
God is genderless, but there is a great absence felt by those who do not have the love of a Father, especially men, who have lost or never known a Father. A horrifying statistic is that about 70% of prisoners in the United States do not have a father in their lives. He may have realized that people lacked this bond and would need to seek God in order to fill that absence.