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Never forget that the Doctor's aunt, High Chancellor Flavia, was named Acting President by the Doctor, who wanted to run away from his own Lord President duties.
She adopted an intelligent cat as an advisor while Acting President. She named this Gallifreyan cat....the Doctor.
So notorious little shit of the family, Time Lord Renegade "the Doctor," ran away from Gallifrey, dumping all of his responsibilities on his aunt, and she responded by replacing him with a pet cat.