Why do dogs (and sometimes cats) walk funny when you put shoes on their feet?
Because it feels weird, I think, is the most effective answer.
Think about how feet work, no matter what the species - they’re designed to be able to expand and compress under an individual’s weight, to squish and change shape as weight is put on them throughout the length of the stride, and then to pull back together as the foot is lifted. Adding a shoe to that totally changes how walking feels (because the foot isn’t in contact with the ground directly) and potentially how it can occur (if the shoe is solid in a way that restricts expansion of the toes). Soft rubber / plastic shoes like the ones that you can get to protect pet toes from extreme weather may not extremely restrict how their feet can move, but they’d definitely feel weird! And if there’s something weird or wrong relating to feet, what does anyone reflexively do? Walk gingerly until you figure it out / get used to it / the thing that feels weird falls off.