By taking your significant other hunting you accomplish a lot of things.
#1 They will become less hesitant to object when you go hunting because they understand.
#2 The ability to enhance an already good relationship by finding a common hobby. (beats the heck out of shopping or gardening)
#3 Educates them to become more conservation oriented.
You can imagine the list can go on and on.

My best advice is to start slow and then work up. I started my girlfriend w/ dovehunting and eventually worked up to deer.
Hope this helps!!!!