I have heard about wealthy people all over the world keeping big cats as pets but those are always kept in cages or their own enclosures. What seems wrong is you claiming that regular people are keeping tigers as pet. Infact people and tigers are more in conflict due to encroachment of humans into formerly forested areas.
Water and ice are made up the same particles and molecules yet the mathematical structure to define the effect of force/pressure is very different - plastic deformation vs fluid dynamics as the example given above
Neither of them is trying to model the universe (that is the purview of cosmology). We are trying to model very particular phenomenon happening in the universe and there is no reason to expect them to modeled using the mathematical structure. The fact that they are is very fascinating.
Crazy thing is very similar mathematical structures is used to define the behavior of a single particle in QFT and of a huge collection of particles in condensed matter physics