Mushrooms are more closely related to humans than to plants.
Fungi, including mushrooms, are indeed more closely related to animals than plants. They share genetic characteristics that plants do not have.
For example, both mushrooms and humans store carbohydrate energy as glycogen, while plants use starch to store energy. Both fungi and insects use the polysaccharide chitin to build cell walls, while plants use cellulose. And mushrooms, like humans, produce vitamin D when exposed to sunlight.