If a worthless small dog attacks your sweet big dog, would you still sue the owner?

My friend's dog happens to be a big, gentle APBT (Mickey is his name) that even befriends cats. It's been obviously trained and raised with love.

However, her neighbor has an aggressive, problematic worthless jack russell terrier. It barks at everyone but people ignore the issue because it's small. That small dog lunged into Mickey and bit him hard enough to leave a small mark, drawing a tiny bit of blood. Mickey backed away and didn't fight back. My friend is still just as upset. She wants to sue the owner. If that was your peaceful dog (with the patience of a saint), would you still sue?
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That small dog got lucky my friend's pittie is sweet. Mickey could've easily killed that Jack Russell Terrier. The owner thinks my friend is overreacting.
If a worthless small dog attacks your sweet big dog, would you still sue the owner?
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