Why should God make a covenant with us?

God gave us the New Covenant for the purpose of our salvation, because he loves us. In the broadest sense, all those who have been validly baptized into the only Church that was ever personally founded by Jesus Christ, while he still walked the earth, are heirs to that covenant, as well as to all the other divine promises.

A covenant is a contract between God and ourselves.  He guarantees to hold up his end of the bargain.  He is not petty, arbitrary, capricious, mean, or evil.  Everyone who complies can receive the third heaven.  If we cooperate, he will even help us become like him.  That's what any good father would do.

THE KINGDOM COVENANT

Due to his faith and obedience, King David was singled out by Jehovah to become party to an outstanding covenant. It was a kingdom covenant that backed up the covenant with Abraham, for it made certain the fulfillment of the promise to bless all nations and families of the earth. “I shall certainly raise up your seed after you, which will come out of your inward parts, and I shall indeed firmly establish his kingdom. He is the one that will build a house for my name, and I shall certainly establish the throne of his kingdom firmly forever.”—2 Sam. 7:12, 13.

The seed that God raised up from David, and whose kingdom he firmly established, is Jesus Christ. “This one will be great and will be called Son of the Most High, and Jehovah God will give him the throne of David his father, and he will be king over the house of Jacob forever, and there will be no end of his kingdom.”—Luke 1:32, 33.

The kingdom covenant is of vital importance to mankind, for it insures the establishment of permanent peace upon earth and just rule for all peoples. God will not fail to keep it.—Ps. 89:33-37.

THE NEW COVENANT

Long in advance, Jehovah foretold the establishment of a new covenant to replace the law covenant after it had served its purpose. Since the purpose of the Law was to lead descendants of Abraham to the promised Seed, Jesus Christ, it was due to end when Christ fulfilled its purpose by laying down his life as a ransom. “Christ is the accomplished end of the Law.”—Rom. 10:4.

It was through the prophet Jeremiah that Jehovah foretold the new covenant. “‘Look! There are days coming,’ is the utterance of Jehovah, ‘and I will conclude with the house of Israel and with the house of Judah a new covenant.’” (Jer. 31:31) Jesus announced this covenant to his followers on the night before his death by saying: “This cup means the new covenant by virtue of my blood.” (1 Cor. 11:25) The blood of his perfect sacrifice validated it, putting it into force. Fifty days after his resurrection it became fully operative when the first of 144,000 spiritual Israelites were brought into it.

The new covenant was not made with fleshly Israel but with spiritual Israel, consisting of Jews and non-Jews. “Moreover, if you belong to Christ, you are really Abraham’s seed, heirs with reference to a promise.” (Gal. 3:29) These spiritual Israelites were given the marvelous promise of being made priests and kings with Christ in his heavenly kingdom. Their being taken out of the nations as a people for God’s name fulfilled the purpose of the covenant. The perfect sin-atoning merit of Christ’s sacrifice makes possible for them the fulfillment of the promise: “I shall forgive their error, and their sin I shall remember no more.” (Jer. 31:34) On the basis of that sacrifice their errors and inherited sin are forgiven and righteousness is imputed to them so they can be begotten as spiritual sons of God.—Ps. 50:5.

The new covenant does not cancel the Abrahamic covenant or the kingdom covenant but is a valuable addition to them that makes their fulfillment possible. Although the 144,000 spiritual Israelites are the only ones taken into it, they are not the only ones it benefits. In due time it will cause blessings to come to a great crowd of faithful people.

By means of these various covenants God has manifested his great unselfishness and love, proving that his greatness and exaltedness do not mean he is not interested in lowly humans. Instead of ignoring them he shows them undeserved kindness. The covenants he has made with faithful humans give us hope for a glorious future on a beautified earth. His word will not return to him “without results.”—Isa. 55:11.

It pleases God to see us trying to please Him and trying to take what He gave us and make something out of it.  We were created in His image, so we are like children to Him.  A Father wants His children pleasing to Him.  So my question is - Are you trying to please the One God who created you?

There's no reason that he SHOULD.

He does so because he is MERCIFUL and KIND.

God wanted people to be with him in eternity. So there is his motive. But more importantly, he wants to prove his word to be true. That's another motive but it really is the main one. God is countering rejection to what he says. And he will succeed. A covenant made by him is a part of his word that he intends to make true. The Gospel is a covenant which is giving imperfect people a chance to take part in that part of his word; his truth, his promises on that side of the equation. 

edit: The qualification is that he chose you personally (he chose first; preordained; prognosticated, limited in advance, Ephesians 1), and that you responded to him personally, in this way:

John 3

18 "Whoever believes (pisteuo- to trust in; to have confidence in) in him is not condemned, but whoever does not believe stands condemned already because they have not believed in the name of God’s one and only Son."