Do stray Cats choose their owners
The short answer is Yes and No.
Remember that adult humans are about 10 to 20 times the size of an average domestic cat. There is a lot of fear, and it takes a lot for a cat to trust a single human being. Moreover, the cat comes with past experience (both as a species, stored in its genetic makeup and as an individual cat with life experience). The better the match between the past experience of a cat and a human it is exposed to, the better the chance that the cat will “choose” that human. In this sense, the stray cat may choose an owner.
Trusting more people than one, may be risky and lack survival value (at least according to the cat’s genetic makeup), thus the cat may focus on one single person as a favorite. However, it seems that cats in general are programmed turn towards the one who to makes the most effort – to talk to them, spend time with them, and play with them. In this sense, the owner chooses the cat by making the effort.
However, on a more abstract level, the concept of choice can be questioned. Something takes place behind our forehead that we have decided to label “choice” or free will (we perceive it as free will or choice). However, free will can be questioned, and our choices can be considered to be the result of our environment – the environment shapes the species behavior by variation, selection and retention (our genetic makeup). Once we are formed, the environment again shapes our development in the womb; once we are born the environment again kicks in, shaping our everyday experiences, and therefore deciding our experience and behavior at every single point in time. Arguably, we humans, and the cats, are 100% under the control of the environment, thus we do not choose.