How is Nick an insider?

As soon as Nick arrives in Long Island, he is accepted as an insider by Tom and Daisy Buchanan, who have multiple connections to him. First, we learn that Daisy is Nick's second cousin once removed, Nick and Tom were at college together, and the three of them once spent "two days" together in Chicago. While Nick says this in a way that makes light of the relationship, these connections matter.
As Nick's recollections unfold, we learn that not only were Tom and Nick at Yale together, they were in the same "Senior Society." We find out as well that the very wealthy Tom "approved" of Nick, and further, that Tom wants Nick to like him.
Further, not only did Daisy, Nick, and Tom spend "two days" together in Chicago, they are clearly from the same social set. We know this because both Tom and Daisy insist they've heard that Nick is engaged to be married, a rumor he denies:

‘But we heard it,’ insisted Daisy, surprising me by opening up again in a flower-like way. ‘We heard it from three people so it must be true.’

Finally, Tom, who has been reading about race, includes Nick as a "Nordic" in his thinking.
Gatsby, for all his wealth and charm, will never gain this kind of acceptance as an insider to Tom's charmed circle. Tom will always treat him with contempt, considering him lower class and non-Nordic.