This part of the Phaedo is teasing out a philosophical nuance, namely the distinction between (what I would call) metrics and objects. You can see Socrates setting that up around 103b, where he says:
You have bravely reminded us, but you do not understand the difference
between what is said now and what was said then, which was that an
opposite thing came from an opposite thing; now we say that the
opposite itself could never become opposite to itself, neither that in
us nor that in nature. Then, my friend, we were talking of things that
have opposite qualities and naming these after them, but now we say
that these opposites themselves, from the presence of which in them
things get their name, never can tolerate the coming to be from one
In more accessible terms, this is the difference between saying "is X" and saying "is Xer than". The example given later using odd numbers is instructive. Clearly 'Oddness' is constructed in opposition to 'Evenness'. That's the first case, in which the concept 'Odd Number' has no meaning except as measured against the concept 'Even Number'. But no specific odd number is defined in opposition to any specific even number: 3 is not the opposite of 2 or 8, 5 is not the opposite of 4 or 6. Likewise one person might be consider tall when measured against one person (i.e., 'taller') and short when measured against another person (i.e., 'shorter'), but no one can be 'tall' and 'short' at the same time.
Put in more modern terms, we can think of a metric as something which shows difference along a single dimension, and an object-class which shows uniqueness by negating all other things. Thus 'hotter' is a metric along the single dimension of temperature: fire is hotter than snow. But 'fire' is opposed only by things that are 'not-fire'; campfires, forge-fires, and wildfires are a unique category of objects that share common characteristics lacked by other objects. Snow is not the direct opposite of fire, though snow is surely included in the world of things that are not-fire.
This of course leads to some confusions. 'Hot' is an object; 'hotter' is a metric. We need (in Socrates' sense) to have some access to some idealized object 'hot' in order to apply the metric 'hotter', but the two modes need to be kept conceptually separate from each other.