Why keep the Golden Rule?

Christ Jesus explains why: 

"Ask, and it will be given you. 
Seek, and you will find.
Knock, and it will be opened to you. 
Indeed, everyone who asks receives, 
and he who seeks finds. 
And to him who knocks, it will be opened. 
Or what person is there of you, if his child asks bread of him, 
he might give him a stone? 
Or even if he requests a fish, he might give him a serpent? 
If you, therefore, being evil, know to give good gifts to your children, how much more will your Father in the heavens give good things to them who ask Him? 
Therefore, all things whatsoever you wish that people should do for you, so also do for them, for this is the Law and the Prophets." (Matthew 7:7-12)

St. John Chrysostom (d. 407) is quite unique in identifying, and drawing hearers attention to, this vital logic of Christ.

"...to indicate that we ought neither to feel confidence in prayer, while neglecting our own doings; nor, when taking pains, trust only to our own endeavors; but both to seek after the help from above, and contribute withal our own part; He sets forth the one in connection with the other. For so after much exhortation, He taught also how to pray, and when He had taught how to pray, He proceeded again to His exhortation concerning what we are to do; then from that again to the necessity of praying continually, saying, 'Ask,' and 'seek,' and 'knock.' And thence again, to the necessity of being also diligent ourselves.
         'For all things,' saith He, 'whatsoever ye would that men should do to you, do ye also to them.'
         Summing up all in brief, and signifying, that virtue is compendious, and easy, and readily known of all men.
         And He did not merely say, 'All things whatsoever ye would,' but, 'Therefore all things whatsoever ye would,' For this word, 'therefore,' He did not add without purpose, but with a concealed meaning: 'if ye desire,' saith He, 'to be heard, together with what I have said, do these things also.' What then are these? 'Whatsoever ye would that men should do to you.' Seest thou how He hath hereby also signified that together with prayer we need exact conversation? And He did not say, 'whatsoever things thou wouldest to be done unto thee of God, those do unto thy neighbor;' lest thou should say, 'But how is it possible? He is God and I am man:' but, 'whatsoever thou wouldest to be done unto thee of thy fellow servant, these things do thou also thyself show forth towards thy neighbor.' What is less burdensome than this? what fairer?
         Then the praise also, before the rewards, is exceeding great.    
         'For this is the law and the prophets.' Whence it is evident, that virtue is according to our nature; that we all, of ourselves, know our duties; and that it is not possible for us ever to find refuge in ignorance."[1]

God Almighty is parenting children to be holy, that is good, kind, thankful, full of praise and joy and peace and love (Hebrews 12). Would any wise parent reward a child for wrong behaviour? Where would that lead?

"For that reason, seeing that also we are encompassed by so great a cloud of witnesses, let us lay aside every weight, and the sin that so easily besets us, and let us run with patience the race that is set before us." (Hebrews 12:1)

"For this reason, girding up the loins of your mind, being entirely sober, hope to the end for the grace that is to be brought unto you at the revelation of Jesus Christ; as obedient children, not fashioning yourselves according to your former lusts in ignorance, but as he who has called you is holy, so you be holy in all manner of conduct; because it is written, 'Be holy; for I am holy.' And if you call on the Father, who without respect of persons judges according to every person's work, pass the time of your sojourning here in fear...." (1 Peter 1:13-17)

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Notes:
[1] St. Chrysostom: Homilies on the Gospel of Saint Matthew, Homily XXIII. http://www.ccel.org/ccel/schaff/npnf110.iii.XXIII.html