I really struggle with this, on the one hand people who have seen them are often very very convinced and compelling, and often tell tales of gamekeepers/farmers who have seen proof to back up what they are saying.
On the other, I'm a sheep farmer living in a very rural community deeply amongst the hunting and shooting fraternity in an area where there are frequent big cat sightings and none of the farmers and gamekeepers who are out 365 days a year in all weathers at all times of night have anything much to say about it.
It's nearly always members of the public who claim to have seen things with little evidence.
The gamekeeper closest to me can tell you on any given day what animals have been around; they track footprints, track scents and poo and have multiple camera traps, infrared scopes etc as do many farmers and gamekeepers across the country. I really struggle to believe that the big cats somehow have managed to avoid all of these and the professional riflemen out most nights in areas heavily populated with deer, but Joe public with a pixilated out of context camera phone can snap them regularly.
No farmer finding a mauled sheep would just shrug their shoulders and move on. Calves aren't disappearing from fields, goats amd pigs arent being snached during the night, even the remains of most dead lambs can eventually be tracked down to a fox or badger hole somewhere nearby.
No dead big cat remains, no big cat roadkill etc
I WANT to believe it but if big cats were anywhere they would be where I live with large open moorland and very easy prey and... they just aren't.