Infants are placed in cars facing the rear because most car collisions occur with the impact to the front of the car. The occupants of the car are thus thrown forward as the car is forced to a sudden stop. In a young infant who does not have good head control and doesn't have much strength in his neck, that forward motion could cause severe and even fatal spinal cord injury, as the head is snapped forward. Infants have very large heads compared with the rest of their bodies and, combined with their less-developed motor skills, they are less able to resist that forward snapping motion of the head and neck. When an infant is facing the rear, his head will already be against the back of the car seat, so in a front collision it just presses further against the back of the car seat.
You mention that you have a convertible car seat, which means he should still fit in it well, even though he is so big for his age. Infants who are that big who are in an infant car seat, rather than a convertible one, would need to move to a larger car seat.
With all the new car seats available, as well as all the new studies showing what the risks are to children in car accidents, there has been some confusion regarding recommendations for appropriate use of car seats. A wonderful site that is maintained by the American Academy of Pediatrics, reviews all the specific recommendations and answers most of the questions that parents have about individual car seat use. You can access that site to get more detailed information.