Gatsby reveals his contempt for Tom Buchanan when he calls him "the polo player." The men had met "two weeks ago," although clearly they knew one another in the scuffles for the affections of Daisy in the past. However, when they were unknowingly "introduced" to one another, "Tom had accepted the introduction as a stranger."
As the small talk continues, Mrs. Sloan wishes Gatsby would accompany her to dinner in New York. Gatsby remarks that he hasn't "got a horse. I used to ride on int the army but I've never bought a horse."
This is infomation is relevant to his later snide remark, calling Tom a "polo player." When it is Gatsby's turn to "introduce" Tom to the party guests, he "took them ceremoniously from group to group: "Mrs. Buchanan...and Mr. Buchanan --." After a instant's hesitation he added, "the polo player."
Note the two digs Gatsby gets in here: not only does he introduce Daisy first (and pauses before he is able to spit out Tom's vile name) but by calling him a polo player, he is implying that he is rich and soft, that his experience with horses did not parallel his own masculine experience of horses in the Army. He is trying to make Tom look as ineffectual and impotent as possible to Daisy.