If you haven't noticed, Sniper Wolf loves Wolves. When she was with the terrorists, they wanted to kill all the wolves that were there, but Sniper Wolf stopped them. She feeds and takes care of the wolves that are there. She calls them her Family.
Metal Gear Solid uses animals as symbolism. Everyone's code name has an animal in the second part. It reflects the person's personality. Snake, Ocelot, Raven, Mantis, Octopus, and Wolf. They all reflects their personalities. Sniper Wolf is a lot like a wolf. Wolves are untamed, they live on their own, with their own pact. Their not like dogs. Dogs are sold off, their tame (most anyway), and domesticated. Wolves don't like to be bossed around. Sniper Wolf is the same way. She joined the terrorists because she wanted to take revenge on the world. She had her own motive. She wasn't sold off, like mercenaries. And as Solid Snake said, "Wolves are noble animals. They’re not like dogs. In Yupik, the word for wolf is “Kegluneq” and the Aleuts revere them as honorable cousins. They call mercenaries like us “Dogs of War”. It’s true, we’re all for sale at some price or another, but you’re different…untamed…solitary. You’re no dog…You’re a wolf."