Call no man father. That is what Jesus said. Now what was that about? Was it a comment on the pervasive promiscuity of men and women; possibly.
"You must call no one on earth your father, since you have only one father, and he is in heaven." Matthew 23:9 Jerusalem Bible
Jesus said that his words were Spirit; that his words were life. If you regard your physical self as who you are; if you identify with your body, then what is going to happen when your body dies? Your consciousness will dissipate along with your body.
By identifying with your spirit by regarding your father as the Eternal Spirit; you are preparing your consciousness to attach itself to the immortal spirit of God and thus to weather the passage of your physical being.
During Jesus’ time on earth the inheritance was passed on through the father. Some households had servants (slaves). The slaves place in the household was not assured not like the children. The slave could be sold or traded. They could be gone at any time. They certainly were not due an inheritance.
Jesus assured us that as the Son of God, his place in God’s house was assured and if he set us free we are free indeed and our inheritance (eternal life) is assured as well.
So if you want to identify with your earthly father; if you are concerned with earthly material things; then your focus will probably be on maintaining the status quo. If you regard yourself as a spiritual being and you look to your eternal reward of eternity with a loving God; then you will want to celebrate Father’s Day commemorating the unity and equality of all your brothers and sisters.