Why was Nick invited to Gatsby's party instead of just being expected to come in The Great Gatsby?

This is something we only discover later on in the text.
You are right, however, to draw attention to the strangeness of of the way in which
Nick, by his own estimation, is one of the few guests who were actually formally invited
to the party that he went to at Gatsby's house. He tells us in Chapter Three just how he
received the invitation:

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I had been actually invited. A chauffeur in a
uniform of robin's egg blue crossed my lawn early that Saturday morning with a
surprisingly formal note from his employer: the honour would be entirely Gatsby's it
siad, if I would attend his "little party" that night. He had seen me several times, and
had intended to call on me long before, but a peculiar combination of circumstances had
prevented it--singed Jay Gatsby, in a majestic
hand.

The intentional nature
of Nick's invitation must mean that there is some kind of reason for Gatsby wanting him
there, and the way in which, when he starts talking to Gatsby, Gatsby is very friendly
and invites Nick to go flying with him, might lead us to believe that there is some kind
of hidden motive to Gatsby's actions. Later on, we discover that this is because Gatsby
had found out that Nick was Daisy's cousin, and thought he could use a friendship with
him to get to her.