Because you can hunt more places at once with less effort than trying to spear of shoot a critter.
Notes:
1) Most likely illegal unless in an actual emergency
2) Use wire so the snares don't release
3) Basic ideas, practice is a must
4) Funnel game trails by placing sticks in the ground to fence in the trail
5) Mask your scent by rubbing the mechanism with leaves/soil, if possible leave for several days before arming
6) Spend as little time as possible near the trail/trap
7) Neck snares should be just big enough for the head of the critter

Notes:
1) Most likely illegal unless in an actual emergency
2) Use wire so the snares don't release
3) Basic ideas, practice is a must
4) Funnel game trails by placing sticks in the ground to fence in the trail
5) Mask your scent by rubbing the mechanism with leaves/soil, if possible leave for several days before arming
6) Spend as little time as possible near the trail/trap
7) Neck snares should be just big enough for the head of the critter