Cats may like to smell shoes for one of the following reasons:
1. Scent: Cats have an extremely keen sense of smell, and they can gather a wealth of information by sniffing objects. Shoes often carry your personal scent, including sweaty feet and oily skin. For cats, sniffing shoes is a way to explore and learn about your scent.
2. Comfort: Cats may find comfort and a sense of belonging in your shoes. Your shoes have your scent, which is familiar and comforting to cats. They may use smelling your shoes as a way to feel comfortable and relaxed.

3. Territorial Marking: Cats are territorial and tend to mark and leave their scent within their territory. When a cat sniffs your shoes, it may be marking them as part of its territory, a way for it to express ownership and belonging.
4. Curiosity and Exploration: Cats are naturally curious animals; they get excited and curious about new objects and smells. Your shoes might be one of the new things that interests them, and they satisfy their exploratory desires by sniffing them.