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He loves Daisy and wants to see her. The reason he wants to do it specifically at Nick’s house is because Nick lives next door to Gatsby, so this would make for an easy setup for her to see his great big house and come over to his place.
He’s afraid that Nick will disagree. Jordan can make Nick sympathetic to Gatsby’s case and vouch for the honesty of this background scene where the two characters fell in love many years ago. Jordan is also a beautiful girl who could possibly convince Nick to agree whereas Gatsby may just offend Nick by this request. Notice Gatsby is CAREFUL! He’s doing whatever it takes
to improve his odds of getting his dream.