Eternal life is not automatic.  The Greeks believed in the natural immortality of the soul, that is, everybody gets to live forever.  This is still popular, unfortunately, even in the church.  The Hebrew scripture does not teach that.  The NT does not teach that.  It teaches that life is a gift from God through His Son Jesus.  It is a result of being in union with the Son, who is Life.  This life comes to us because of the resurrection of Jesus from the dead.  We live “in the hope of eternal life, which God, who cannot lie, promised long ages ago” Titus 1:2 (NASB).  To have the Son is to have the very quality of life that exists in God.  Otherwise, there is no immortality.