Quick answer: You do not have to hash the inputs to Ed25519 because hashing is already part of Ed25519 itself. If you do hash inputs in advance, you become vulnerable to collisions in the hash function you use.
This rule does not make sense, period, because hashing is an integral part of a secure signature scheme. It is a design principle to use a hash function to compress a message into an element of a mathematical structure that can be combined with a private key to yield a signature verifiable by the related public key. This was first described by Michael Rabin in 1979. Today, every serious signature scheme involves a hash of the message as a first step, with some variations. Any system or textbook that tries to separate the steps of ‘hashing and then signing’ is dangerous.
Here's an example of an RSA-based signature scheme: A signature on a bit string $m$ under a public key $n$, a large integer with large prime factors, is an integer $s$ such that $$s^3 \equiv H(m) \pmod n,$$ where $H$ is a random function from bit strings to positive integers below $n$.
The hash $H$ is an integral part of this signature scheme because if you didn't use it, and instead used the equation $s^3 \equiv m \pmod n$, then I could trivially forge the signature $s = 0$ on the message $m = 0$, or $s = 2$ on the message $m = 8$. The use of $H$ means I can't use the advanced technique of computing integer cubes on my pocket slide rule to forge signatures, because I don't have a hope of finding an $m$ with any prescribed hash value.
In the case of Ed25519, a signature on a bit string $m$ under a public key $A$, a point on an elliptic curve, is (roughly, with details of encoding and cofactors elided; see the Wikipedia article for more detail and references) a pair $(R, s)$ of a point $R$ on the curve and an integer $s$ such that $$[s]B = R + [H(R, A, m)]A,$$ where $B$ is a standard base point on the curve, $H$ is a random function from two curve points and a bit string to an integer below the order of $B$, and $[s]B$ etc. denote scalar multiplication on the curve.
Hashing a per-signature randomization and the public key together add some security beyond the simple RSA-based scheme above: hashing in per-signature randomization obviates the need for $H$ to be collision-resistant in practical realizations (the lapse of which in practical systems using MD5 has had serious consequences), and hashing in the public key mitigates multi-target attacks and prevents key malleability—finding two distinct keys under which a signature is valid.