Wow -- a really interesting question. First, I would look at Orwell's political message, read the analysis of the characters, and then make a decision based on that information. I refer you to the enotes link below where you can go and get the full descriptions.
First, what is the political message of Animal Farm? Orwell was completely against totalitarianism and for Democratic socialism. A totalitarian government completely controls the government and the people. This novel was written as a reaction to Orwell's bitter disappointment with the Russian Revolution that was supposed to establish a republic for the people. Instead, the revolution established a totalitarian government. His novel represents his opposition to any and all totalitarian governments. He uses the animals in his book to symbolize the players involved in such a totalitarian state and how such tyranny can happen in any country. Orwell warns us that in order to prevent this from happening, the average citizen has to be unwilling to blindly follow the crowd (the sheep) and be aware of propaganda (Squealer) spread by a country's government. We have to be aware of what our government is doing and be willing to challenge anything we consider unjust. We cannot naively believe everything we are told (like Boxer).
Since the animals symbolize the corruption of power in a totalitarian state, it isn't easy to find a sympathetic character among them. This is where you base your answer on your own feelings after reading the character analysis. Two characters come to my mind, however.
Boxer, one of the two cart-horses on the farm, represents the common working class who naively accepts what is happening. Boxer thinks by working hard, he will get ahead and be protected by the government. In the end, Boxer is sent to be killed because he can't work any more. Is he a sympathetic character?
Clover, the second cart-horse, also represents the working class. She tries to get the other animals to see the reality of what is happening, but she doesn't get far in her efforts. She runs after the van taking Boxer away to slaughter, but she's unable to stop it. She represents those citizens who should know what's happening to them, but due to laziness or just not caring, she does nothing. Is she a sympathetic character?
The other characters really don't offer much of a choice. The pigs are ambitious for power, the sheep are the ignorant followers, and the raven represents organized religion that Orwell opposes.
This is the type of question where your teacher wants you to come up with an opinion based on the facts of the story. You can probably make a pretty good case for Boxer as a sympathetic character since he is naive and trusting. I wish you well in your efforts to answer. Go to the enotes' link, and I believe the information there can give you what you need to come up with an informed answer, which is what your teacher is trying to get you to do. Good luck!