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What's the largest animal a person could beat in a fight
Assuming the person is of average strength and without any weapons, the largest animal they might be able to fend off would likely be a medium-sized dog. Any larger or more powerful animals, such as bears or big cats, would likely have too many advantages in terms of strength, speed, and natural weaponry.
If you consider using tools or weapons, the size of animal that can be subdued increases but so does the ethical and legal complexity. Note that this isn't a recommendation to engage in fights with animals; it's simply a hypothetical evaluation of human capabilities.
URLs for further reading on animal strength compared to humans: