Neither of these terms are making an assertion. We have already seen why this is the case for “ant.” However, it may be more tempting to think that “The ant which walked along the ground in a quick fashion” is making a claim. It seems that we are saying there is an ant that walked along the ground quickly. But in fact, we are saying only what it means to be in the category “The ant which walked along the ground in a quick fashion”. Namely, in order to be a member of this category, an object must be a particular ant that walked along the ground in a quick fashion.
We are not stating anything about this ant; not even that this ant exists. It is in this sense that we are not predicating anything of it. It might be helpful to compare “The ant which walked along the ground in a quick fashion” with the following proposition: “The ant which walked along the ground in a quick fashion is over there”. Only the second of these predicates something of a subject, this particular ant; accordingly, only the second of these can be true or false.
“Expressions which are in no way composite signify substance, quantity, quality, relation, place, time, position, state, action, or affection… ‘Double,’ ‘half,’ ‘greater,’ fall under the category of relation.”
Aristotle, Categories (W.D. Ross, 1952)