If we assume that a fluid is a continuum then if we have for example a cup of tea and we stir the fluid then there will be a point in the fluid that is on the same location before and after the stirring.
Now, a practical fluid is not a continuum although it is for many practical situation in fluid mechanics.
Does this influence the statement much? Is there for example a small box where the particle will be in (which is somewhat in the same magnitude as the size of the particles) or does the complete statement break down?