
The conclusion from a couple of PhD experts, Dr John Bradshaw (Cat Sense) and Dr Desmond Morris (Cat Watching and many other books on animal and human behavior), is that cats do not think of us as equals. The domestic cat thinks of us as (1) surrogate mothers and/or (2) kittens and/or (3) superior creatures depending on the circumstances and theory!
Kittens
However, it is Dr Morris who suggests that cats sometimes think of as kittens when they bring prey animals home as if they are bringing prey items back to the natal den. But Dr Bradshaw disagrees with this because in the wild when cats bring prey back to the den, it only occurs when a female has kittens and she wants to teach them how to kill prey and/or feed them. Females and males without kittens don’t do this. Also, female cats don’t treat humans as their kittens on other occasions.

Size difference
There is also the problem of size differential. Dr. Bradshaw thinks that it is implausible that cats think of humans as their kittens because of the size difference. This presumes that cats are fully aware of the size difference and mentally process it.
Substitute mothers
However, he agrees that humans can be a mother substitute i.e. a surrogate mother. On this he agrees with Dr Morris.
There are many cat behaviours which support this theory, all of which are based on the fact that humans provide almost comprehensively for cats’ every need (in good homes).
And cats take the size difference into account because, for example, they jump up to head-butt our hand when it is offered to them. Or they jump up onto furniture so that they can communicate more or less at the same physical level. They deposit scent on our legs by rubbing against us but don’t expect us to do the same in return. And also, they lick us as an altruistic gift once again not expecting it in return. That is his argument.
Personally, I would disagree with that slightly because when we stroke and pet our cats, from their perspective we are licking them and/or depositing our scent onto them. Stroking has a multipurpose function. So perhaps they do expect reciprocation and they feel that they get it.
Humans are perceived as being superior
Nonetheless, he believes that these feline actions indicate that cats accept that we’re much larger than them which also inculcates that from the cat’s perspective we are superior to them. This is reinforced by the fact that we control their food supply.
Personal thought
Personally, I think of my cat as an equal. I interact with him on this basis. I am sure that this helps him to regard me as an equal too. I think it happens quite a lot but the underlying relationship is of parent/kitten which undermines the concept of equality. The parent is superior as they are the providers.
Conclusion
Dr. Bradshaw, therefore, concludes with the following statement in answering the question in the title:
“A definitive answer on how cats perceive us thus remains elusive; for the time being, the most likely explanation for their behaviour towards us is that they think of us as part mother substitute, part superior cat.”
Dr Bradshaw in Cat Sense
Bringing prey home
Therefore, he rejects the Morris theory and argues that cats bring prey home for a practical reason: they can eat it at their leisure without any competition from other cats or other animals outside the security of the home (provided the other resident cats are not in competition, if it is a multi-cat home!)
Once they have the bird or mouse in the home ready to eat after it has been killed in the home or brought in dead, they sometimes don’t eat it because they change their mind and eat commercial cat food instead. Dry food thanks to the tasty coating that is sprayed on the kibble can be quite addictive.