I would sit down with him when things are calm and tell him you want to talk about school - make sure that you are willing to look at both opions if he can talk with you calmly. Ask him why he wants to stay at his old school. It may be friends, it may be school rivalry, it may be what he hears about the new school from kids at his old school (believe me, in Jr High and High School we talk about the 'snotty' schools and the 'gang/drug' schools, etc). It may or may not be correct, but honor and validate his opinion, even if you decide to have him go to the new school.
In general, as long as you are in the district, get him to school on time, and he has good grade, there should be no problem with him staying at the old school. On the other hand, forcing him to the new school MAY (not will) cause him to feel isolated, friendless, or insecure. There are so many changes going from 6th to 7th grade anyway and a new school at this point may just be too much.