Read John 14:4-11.
The term “father” is used exclusive of God the Father, and to be honest, I am not aware of a clear instance when Jesus was called “father” (although possibly 2Cor. 1:3). Despite that, Jesus often made statements that showed His equivalency with the Father. The passage today is one such incident. Jesus makes others such as “I and the Father are one.” (John 10:30) He takes on the same authority as the Father (John 10:18). So while Jesus may not be referred to as the “Everlasting Father”, He certainly takes on the calling of the Father, and I suspect that one day the unity of the Father, Son, and Holy Spirit will take on much, much greater meaning when we live in eternity with Him/Them and Jesus will be seen as our Everlasting Father.
This particular title (Everlasting Father) likely denotes a contrast between our mortal fathers and our eternal Father. Our Everlasting Father is just that — everlasting. He will never fade away or become any less of a father. He will never give up that place in our lives. If you’ve ever lost a father, you know the pain associated with the loss of someone so significant. I imagine there is a feeling of being left on your own, that the one that you could depend on to be there for you is now gone. And though that may not be your experience, the loss is regardless a difficult one. Our heavenly Father is everlasting. And we will never be alone. He will always be there because He is eternal.
To consider: Have you ever looked at Jesus as your Everlasting Father? He cares for you as a father. He helps you as a father should. He guides you and sustains you as a father should a child. Has there been a time in your life when He has been like a father to you? Have you ever felt forsaken? In those times, remember He is our Everlasting Father. (Note: The famous “footprints” poem comes to mind here. You can find it here: http://www.barefootsworld.net/footprints.html if interested.)