I'd imagine that the thinking goes that emotion requires self-reflection. Being depressed isn't really a thing if I don't even realise it's me that is depressed because I have no conception of self.
If there is no higher function that can decide to suffer pains then pain is irrelevant, reaction is not emotion.
This method is believed to be highly imperfect though as not all animals rely on visual perception as their main info channel. So some animals that do not pass the test may be self-aware, we just don't know how to research it properly.
It would surely seem many of human emotions are based on reflective properties and certain thoughts being at the basis of the subjective reality in which these humans consequently find themselves, in which it "makes sense" for the emotion to occur. We "think" ourselves into emotions about work, about our homes, about society, politics, video games, etc. etc.
I do think that there is a place for emotions though, even aside from those conditions: many times people feel certain emotions, but they don't know themselves that they feel it, or what they feel. This is evident in psychotherapy, a lot of the time the work itself is simply to get the person to understand what they are feeling. This would suggest that feeling of these emotions somehow exist, in some sort of lower level emotional substrate, before the symbolic consciousness has acquired a view of these processes. Such emotions and their substrate likely is present in animals as well.
It is logical to assume, that for any emotion to exist, there has to be some ground "intelligent"(on some level) understanding of a certain reality - if one feels sad, there needs to be something going on in the subjective reality of the subject (like being separated from a loved one), to which this emotion should be reacting, and this event needs to have certain properties and not others, and there needs to be something in the subject that understands this difference. But this understanding does not need to be based in symbolic intelligence, it surely seems like it can be hosted in the aforementioned pre-symbolic substrate, which animals seem to share with us.
A cat obviously feels and "knows" somehow when it is being separated from a loved one, be it another cat or a human. Assuming that the cat does not have much of a symbolic intelligence, the fact that it can still do that, it means that there is a system in the cat which can nevertheless track how close it is to a loved one. So if there this system, that could likely serve a purpose of being this substrate on which the emotions are reacting.
Thus developed symbolic intelligence is not strictly required for emotions to occur, assuming there is another simpler intelligence to track the subjective reality, and it sure seems like many animals do have this.
(Of course the open question is how "much" of these respective types of emotions is present in humans, because it would make a difference for whether we would think humans are more emotional in general than animals or not.)