Not trying ot put you on the spot but here is my "whys" to your questions:
Yeah, I'd never shoot a fox unless it was raiding muy chicken coop!
There are SOOO many cougars in southern BC that it would amaze you. Killing a few is not a bad thing, in fact it's encouraged to help the deer populations. Plus- cougar meat tastes good if you prep it right
There are SOOO many wolves in all of BC that it would amaze you. Killing a few is not a bad thing, in fact it's encouraged to help all ungulate populations.
Grizzly populations are the most scrutinized large mammal in BC. If there is a season, it's not a conservation concern. The hunting of grizzly is also heavily scrutinized.
Not alot of lynx around here but plenty of bobcat. No conservation concern, again.
Of course, it's up to you what you hunt, just giving some pertinent information about those species.