In The Great Gatsby, why did Gatsby want Daisy to see his house?
Daisy is beautiful and comes from money. Having grown up in this social class, she has been groomed to seek out a husband with money and prestige. Gatsby is completely aware of this. Despite the superficial component of Daisy's concept of a "good match," Gatsby is still enamored with her. Consequently, to appeal to Daisy in every way, Gatsby knows he must accumulate wealth and social status in order to be a good match for her.
In Chapter 5, when Gatsby has Daisy and Nick over to his house, he is clearly showing these accomplishments off and Gatsby judges his own success through Daisy's eyes.
With enchanting murmurs Daisy admired this aspect or that of the feudal silhouette against the sky, admired the gardens, the sparkling odor of jonquils and the frothy odor of hawthorn and plum blossoms and the pale gold odor of kiss-me-at-the-gate.
He hadn’t once ceased looking at Daisy, and I think he revalued everything in his house according to the measure of response it drew from her well-loved eyes.
James Gatz became Jay Gatsby, which included all this wealth, in order to impress Daisy. Logically, he measured his wealth, less in terms of his own personal success, more in terms of the effect it has on Daisy.
Gatsby, of course, wants to show off his home and possessions to impress Daisy. However, the author F. Scott Fitzgerald also wants to introduce the reader to the house because this is where Gatsby and Daisy will be conducting their love affair. Gatsby could hardly have considered having assignations with Daisy at Nick's little house. It would have seemed sordid, and it would have made Nick look bad--like a procurer or an entremetteur. (Frankly, Nick looks bad enough as it is, letting himself be used by a gangster as a go-between as he does.)
Gatsby's whole dream has been to meet Daisy again and to get her into his house. It is a moment of triumph when she crosses his threshold. After this episode, it will be easy enough for the reader to imagine them meeting there together--and it will be in a setting that is worthy of such a rich, gorgeous, spoiled woman. The affair that goes on between Gatsby and Daisy in luxurious surroundings will be in contrast to the affair between Tom and Myrtle carried on between a garage and a cheap apartment.