Well even on not being rare, lynxes are stalking predators. Given what noisy clumsy travels us humans are and their keen senses, one is lucky to see a lynx. Since firstly they are always stalking or hiding just naturally and specially so hiding upon most likely spotting human way before human spots them. One could go right by one and not notice it. We aren’t on their menu given our size and not being normally encountered prey species. Also as stalkers unless it is something like a mother lynx protecting its young, it won’t make itself known. Far rather hides and let’s you pass without encounter. Since one less risk of the lynx getting injured in fight, if it can’t just hide away and go unnoticed.

Though on top of that some species of lynx are very endangered.