Developing quantum algorithms to simulate fluid dynamics has become an active area of research, as accelerating fluid simulations could have significant impact in both industry and fundamental science. While many approaches have been proposed for simulating fluid dynamics on quantum computers, it is largely unclear whether these algorithms will provide speedup over existing classical approaches. In this paper we give evidence that quantum computers cannot significantly outperform classical simulations of fluid dynamics in general. We study the incompressible Euler equations, which model ideal, inviscid fluids. We show that any quantum algorithm simulating the Euler equations requires exponentially many copies of the initial state, in terms of simulation time, in the worst case. This lower bound holds for the task of preparing the final state, and a similar bound holds for history-state preparation. To prove our lower bound, we show that instabilities enable fast state discrimination.