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When the World is referenced in the Bible it can mean different things:
--- The Earth
--- The People on the Earth
--- Unbelievers
--- Value systems and philosophies

Accordingly, we need to Understand who or what is being referenced by the word, World, in order to Understand the meaning of the Scripture at hand.
Whether we can Love The World on not depends on what is meant by World and the priority of that Love with respect to God.

For God so Loved the World, that he gave his only begotten Son, that whoever believes in him should not Perish, but have Everlasting Life. - Joh 3:16

What World is John Speaking of?
The Earth and all the people born into Humanity.

God is Love and Love is of God.

The World was Created by God and it is Good. We know that man chose Rebellion against God and so Humanity became Evil. But God Loves the people of this World and so sent Christ Jesus to Redeem it and us.

Love is what led Him to be born as a Human, to suffer and die for us.

The Gospel is Heard and those who are hungry are lead by the Holy Spirit to Believe and Receive the Truth.

The Truth sets us Free from Sin, from Death and Hell and brings us to Eternal Life.

If you were of the World, the World would Love his own: but because you are not of the World, but I have Chosen you out of the World, therefore the World hates you. - Joh 15:19

What World is Jesus talking about?
He is talking about the World in Rebellion against God that has aligned itself with Satan.

The World of Carnal Minded people cannot Fellowship with the Body Of Christ containing Spiritual Minded people and vice-versa.

I in them, and you in me, that they may be made Perfect in one; and that the World may Know that you have sent me, and have Loved them, as you have Loved me. - Joh 17:23

The World He is Speaking of is the people in the World - particularly those who have not heard the Gospel.

In Oneness with God through the Holy Spirit we demonstrate the Spirit Fruit and Spirit Gifts testifying to the Lordship of Jesus Christ.

For Demas has forsaken me, having Loved this Present World, and is departed unto Thessalonica; Crescens to Galatia, Titus unto Dalmatia. - 2Ti 4:10

The World that Paul is Speaking of is the World that God created - the Blessings of Earth and the way of Life that most people enjoy.

Paul did not say Demas had forsaken Christ - only him. Many Christians do not commit to the Work of Christ as Paul and Timothy did. They are more like Demas who having a love of the present World are not willing to sacrifice the transient pleasure for the greater Glory.

Love not the World, neither the things that are in the World. If any man Love the World, the Love of the Father is not in him. - 1Jn 2:15

What World is John Speaking of?
Is he Speaking of the Earth that God created?
Is he telling us not to enjoy the Blessings of God's Creation?
No, he is Speaking of the Evil that is in the World.

When we see what is in Heavenly Places our Hearts are forever oriented toward Him who fills Heaven and Earth with His Glory. Carnality is base and has lost its appeal.

Behold, what manner of Love the Father has bestowed upon us, that we should be Called the Sons of God: therefore the World knows us not, because it knew him not. - 1Jn 3:1

What World is John talking about?
He is talking about the people on Earth who are Carnal Minded having never Received the Gospel of Jesus Christ.

Those who are Carnal Minded cannot Understand those who have become Spiritual Minded by Receiving the Truth and being Born Again.

The Glory of Christ is what He willed and accomplished for us by enduring the Cross and raising Himself from the Dead - Sonship in the New Birth by His Holy Spirit as joint Heirs of all that the Father has.