Perhaps what Plato means is that the traditional scientific way of thinking fails to explain everything about life, especially the root cause of life (consciousness). Not that science itself is useless, but simply that it fails in this regard and thus may not be as close to "truth" as we've all been brainwashed to believe.
Science means different things to different people, but generally it's commonality lies in a strong faith in materialism and the physical world being "all that exists". The scientific method itself may not be flawed, but the scientific paradigm, or way of thinking, is strongly linked to the belief in the physical being all that exists.
Since consciousness and 'life' exists, the above belief must be fundamentally flawed. The logical conclusion then is to call into question the validity of the scientific paradigm of reality, since it rests primarily on an extreme faith in the physical world.
Edit: I am also free from the limitations of science.
