There are larger predators like lions featured heavily in cave paintings and other forms of the earliest human art for a reason. We have never hunted predators

There are larger predators like lions featured heavily in cave paintings and other forms of the earliest human art for a reason. We have never hunted predators like bears and big cats as a primary food source, but a willingness to defend humans and our food with hand weapons is actually a skillset actively practiced until very recently in societies like the Maasai. The Human Planet docuseries has a pretty incredible scene where hunter gatherers coordinate to steal a kill from an entire pride of lions. It makes you see why people on the other side of the world in highly industrialized societies would find it to be an adrenaline rush to hunt the biggest, baddest looking animal they can find (not that I do this personally). You're completely right that the desire to hunt a tiger isn't really logical or necessary, I'm just pointing out that it is not psychologically aberrant that some people (mostly men) would find it satisfying to do things like that as a thrill-seeking activity.