To goad the media into bringing this story to the forefront. It is a very strong indicator of future behavior and at the same time an extremely emotional subject that millions of people will identify with. If enough people sign this petition it could make a real difference in the outcome of the election.
Mitt Romney treated his dog Seamus in a heartless way, lacking compassion and concern for his family dog's welfare and feelings — not to mention it was legally animal abuse. He then defended his actions. This is a strong indicator of how he will care for the American people if elected. People tend to treat people the same way they treat animals.