Please don't listen to your boyfriend at all. Normally when you have sex during your period you CAN'T get pregnant.
The only time a woman can get pregnant is during ovulation, which occurs approximately midway between periods. Keep in mind that sperm can live in the woman's body for a few days and that it takes a few days for the egg to decend so there is a range of time every month in which you can get pregnant. Also a woman's period isn't always a predictable thing. Ovulation could occur during your period simply because your cycle is changing. THERE IS NO SAFE TIME TO HAVE UNPROTECTED SEX.
I would encourage both you and your boyfriend to read up on how the reproductive system works. Also start reading up on women's health and how various forms of contraceptives works.
Here are some links that you should probably read through before you even consider giving in to your boyfriend.
Know what you're getting yourself into and how to take care of yourself before you do anything. You are the only one responsible for taking care of yourself. Don't trust what any guy tells you, not even your boyfriend. He wasn't even right. Look things up for yourself. Call Planned Parenthood for information. Don't just take the word of a horny teenager. They'll say anything to get laid.