Final answer:
Gatsby calls people 'old sport' to establish familiarity and fit in with upper-class society, while Tom mocks him for it as a way to assert his own superiority. Gatsby uses 'old sport' to fit into the upper class, while Tom sees it as evidence of Gatsby's inauthenticity.
Step-by-step explanation:
In F. Scott Fitzgerald's The Great Gatsby, the character Jay Gatsby frequently calls others "old sport" as a way of showing friendliness and affinity, in an attempt to fit into the wealthy class he seeks to be part of. This use of language is part of his fabricated persona, as he tries to embody what he believes is the vernacular of the affluent social circles he aspires to join. Tom Buchanan makes this an issue because he is suspicious of Gatsby's background and sees through Gatsby's attempts to appear well-bred, thus perceiving "old sport" as an affectation that betrays Gatsby's lack of authentic high societal upbringing.