taking a break, I really think the best way to let him know that is by telling him straight out, but politely of course, that you wish to have a strictly in-school and only school-related, relationship.
About another issue, I personally feel that it is not nice to give anyone the cold shoulder for a compliment, Jew or non-Jew. There are other ways to give the message to “back off” that are more polite. Giving the cold shoulder can be viewed as rude, and can possibly lead to a chillul hashem.
And I happen to think Avigail is a very pretty name.