A cat owner asks, “Why would my cat steal my shoes and hide them under my bed?” The question could equally apply to other items but shoes are highly suitable because they smell strongly of the owner.

I tried to verify my answer in the reference books that I have without success as there was no information on this form of behavior. I am reliant, therefore, on my own thoughts on this subject and would welcome the thoughts of others.
When you see a domestic cat carrying, for example, a slipper in her mouth and taking it to a safe place, what do you see in terms of domestic cat behaviour?
Moving kittens
It looks very similar to a female cat carrying her kitten to a safe den. Cats often move their kittens to new dens to improve their safety.
Carrying prey
Another form of domestic cat behaviour that this looks like is a cat bringing prey into the house after a hunting expedition. When cats do this they sometimes find a quiet, safe place to devour the mouse.

Confused feline behavior
My conclusion, therefore, in answering the question is that domestic cats are expressing their innate behavioural instincts in a slightly confused way. They are living in an unnatural environment and sometimes do not have the opportunity to properly express their desires. Hunting is an ever present desire and for a female cat mothering is also something which comes naturally to them.
I would suggest, therefore, that when a cat steals her owner’s shoes and hides them under a bed they are either mothering their kitten or bringing in prey. It could be either because the cat is not thinking that it is one or the other. This is instinctive behaviour and in the cat’s mind she is doing either of these things without rational thought.
It is important to recognise that rational thought is absent in this behaviour. If it was present a domestic cat would not do it because it does not serve its purpose. The only purposes this behaviour serves is to relieve the need to express innate desires in an adult domestic cat.
Kleptomania, stealing or attention seeking?
Some commentators and experts have described this feline behaviour as kleptomania. I do not believe that that is correct. It fits in nicely with human behaviour but I think it is mixing up the behaviour of two species of animal.
Neither is it “stealing”. Stealing is a human concept. To call this stealing is to anthropomorphise the domestic cat.
Finally, one expert believes that this is a form of attention seeking. That thought does not appeal to me either. I disagree with them.
Animal Planet’s Must Love Cats video of Dusty in action. So funny. https://www.youtube.com/watch?v=xhRW4WmfrDA
I love the phrase “to relieve the need to express innate desires”. That’s good and I think it nails it better than anything else, and I agree with the other thoughts but I wonder it there’s something going on as far as the cat wanting to do something, there’s the desire (“I want this thing”) and there’s the innate behavior “ability” that the cat can employ to do something about it. They don’t have much of a skill set but they do problem solve and think in terms of cause and effect; and they can string a number of actions and events together for a purpose. It could be stipulated that it’s thinking “this needs to be moved” because that’s what it does to it, but is it a knee-jerk reaction or is there an actual thought behind it? Is it a handy behavior looking for a way to be expressed or a desire inspiring a behavior to be used? Which is dominant or primary? Which initiates the other? It knows it can’t eat it (not prey), nor does the inanimate object need protecting (not a kitten), nor does anyone else probably want it (I have seen cats get possessive about another cat playing with their toy), it just wants it (odor is likely a factor. I’ve seen my cats bury their face in my shoes) and wants to do something about it, like a dog would chew it up or bury it in dirt. It’s the same difference as what Michael said I guess… I’m just trying to understand whatever thought process might be involved and from the cat’s point of view. I do think that the idea of “mine” or “I want this” is the primary motivation, but for a purpose? Does it think that? I’ve seen so-called klepto-cats online and it’s hilarious, (the little hoarders) but I don’t recall having one that would do that and only occasional desires to fetch, the purpose being to play with me. And maybe purpose is too strong a concept for animals but who knows? Bottom line is this stuff fascinates me and I’ll keep wondering about what makes cats tick the rest of my life. Sorry this was a long comment.
Oh yeah, here’s the case of Dusty the cat burglar from San Mateo, Ca. A rare case of a klepto-maniac cat. I don’t think it’s the same as a regular cat moving your shoe. It’s just similar. https://en.wikipedia.org/wiki/Dusty_the_Klepto_Kitty