"It's about loving one another and sharing the same desire."

Not quite deeply enough. 

It's about sharing the same will with the Father.

People use desire here too cheaply.   A flutter of the heart.

It's far more substantial than that.

In God, His Divine attributes of heart, desire, will, mind and work (love, the Cross for instance) are totally united and integrated, fused.  No division, fraying. Unity Himself. 

All united and working toward the good and the true (intellect). 

That's why a Catholic's job is to do the same sort of "rectification" of mind, heart, will, every day until we die.  Discernment, prayer.

Given Original Sin, there is no permanent or natural unity among these faculties of our "personness".  It takes work, daily work. It also takes grace from God.   Constant. 

That's why we have the Sacraments, that's why we have prayer..so we can get closer to the will of God, converting and rectifying more and more of our life into an act of union with God's will.