Why people consider Brown university to be an ivy league university?

Brown University is considered an Ivy League university because it's a member of the Ivy League athletic conference. The Ivy League is primarily an athletic association, but its eight member schools – Brown, Columbia, Cornell, Dartmouth, Harvard, Princeton, University of Pennsylvania, and Yale – are also all highly prestigious, historically significant, and selective private universities. The athletic association's prestige has, over time, become inextricably linked to the academic reputations of its member institutions, solidifying their collective identity as "the Ivy League." Therefore, Brown's membership in this athletic conference is the fundamental reason it's considered an Ivy League university.