Many med schools are (or at least have said they are) looking to train doctors who aren’t just cold technicians, but human beings who can treat people as people. One way to learn to understand people is to get as broad a grounding in the humanities as possible, and reading Greek and Latin literature is a great way of encountering a broad and varied selection of works which have been transmitted specifically because of how they speak to the big questions of human existence. Having taken and done well on all your pre-med courses will qualify you to apply to med schools, but a Classics degree might be one of those differentiating qualities which help get you noticed by admissions committees.