Meanwhile, I couldn't help but think of Yoda's advice to Anakin after Anakin told Yoda about his visions of the death of a person close to him in the Revenge of the Sith: "The fear of loss is a path to the Dark Side. ... Rejoice for those around us who transform into the Force. Mourn them, do not. Miss them, do not. Attachment leads to jealousy, the shadow of greed, that is. ...Train yourself to let go of everything you fear to lose." Now, I found Yoda's advice to not be very helpful or comforting, and it clearly doesn't work for Anakin. Still, it seems that Yoda was explaining a similar idea to Anakin that Jesus was teaching to his Apostles.
Nothing in this world is permanent. Putting our faith and trust into the impermanent pieces of this world will only lead to suffering. Even those whom we love above all others will one day pass away. It is in not accepting the transitory nature of this reality that we bring ourselves greater suffering. Placing our trust (our love) in God allows us to transcend the pain and cares of our mortal world. This allows us to bear the many tragedies that befall us in life, and prepares us for the life that follows. This request of Jesus is not one of selfishness on His part, but rather a path for our own redemption.
According to Matthew's Gospel, Jesus will later his Apostles to treat all people like they would treat Him. Think of this; He first tells them to love God more than anyone else in the world, and then instructs them to treat everyone they meet as if they are Him. That love, that ultimate love that He requests of us, He asks that we share with everyone. This sort of love is not the love brought through attachment, control, or ownership, but a love freely given.