Denial. Serious denial.

Perhaps coupled with low self esteem.

And even the "blood is thicker than water" saying.

Essentially your fiancé is telling you that you MUST like someone who treats her like a dog. If you truly love someone, why would you have an ounce of respect for another who treats them worse than a dog!?!?!

I wonder why your fiancé puts up with such crap?

I'm gonna go out on a limb here and say that her sisters got something mental going on. Maybe your fiancé has a bit of that bonding with abusers syndrome that sometimes happens?

Either way, this is a very messed up situation. I suggest therapy. She's essentially putting the blame on you for a failed relationship with her sister when it's not your fault!