Accoding to Brin & Stuck's textbook (link to the exact place on google books):
Equicontinuous homeomorphisms are not expansive.
But how about $(\mathbb Z_n, R_1) $ where $R_1(x):=\text{mod}_n(x+1)$?
It's minimal and not sensitive, therefore equicontinuous. It's a homeomorphisms. And it's expansive.
I must be missing something but I can't find out what. I've found the quoted statement in other sources too (e.g. in Brown's text "Ergodic theory and topological dynamics") and none of them seem to make any assumptions that would have explained the "counterexample" (e.g. that $X$ needs to be infinite).