It's a mix of things and speaking for myself, deer are beautiful animals and if I am going to take the life of animal for food it is only right and proper that I do it humanely and that the venison will is recovered and used properly. Ditto for ducks, geese and game birds. Personally I don't like pigeon to eat and actually I don't like the featheriness of pigeons - pheasants are bad enough, so I don't shoot them. I do shoot foxes on ground that I manage, more because they take lambs, but I don't like shooting foxes unless I have to. Again I do want ensure it is a clean kill.
We do live on a crowded little island and many people will distressed finding a dead deer or fox, so it is important that any remains are disposed of discretely. I must admit did see foxes hung on a gateway - first time I had seen this in a very long time and did think it was somewhat unnecessary and just adding fuel to those who don't understand the country side.