Walking in circles

When I watch a cat that is walking or running, it does so in a directly forwards motion. It knows where it is going. They say – so I have heard – that if you put a person into a featureless desert and told them to walk their way to safety that they would eventually end up roughly where they started because their stride is uneven and favours one side. I have never been left in such a situation – though I have been in a desert – so I have to take what is said as something close to the truth. Maybe this lopsidedness is because we are right / left handed. Maybe. And maybe this has nothing to do with this: why don’t dogs walk straight ?
Winston does go forward – with a surprising momentum – but while doing this he is also going to the right. It’s as if he were asked to walk / trot North but ends up on a heading on NNE. Why ? Are dogs right-handed ? I haven’t seen a dog that veers to the left (voluntarily that is). Why would a dog have one dominant side for walking or doing anything else ? Apart from the begging thing with the paw that most dogs I’ve known do, for what other reason would they have a dominant leg unless they are right/left handed ? Do wild dogs have such favoured limbs ? Has Man encouraged this through the desire to make dogs beg ? Did dogs that did not beg become extinct due to natural selection (and hunger) so limb favouritism become ‘de riguer’ ? It’s not like they ‘high five’ when they meet either is it ? Or maybe it’s just Winston.