As the others have said, parents are often worried about their children's choices of partners. Nothing they say is going to dissuade you from seeing him because you're in love and you see yourself spending the rest of your life with him.
Four months is still very early in recovery, and the chance of relapse can be high. I suggest you tell your parents you're not rushing into anything, you're just seeing him at this stage and are not naive. Then really follow your own advice and take it slow, give him time to work on himself without an intense relationship to distract him.
You don't say much about his history. Some people have a relatively short period of addiction before their inner self-esteem asserts itself and they are able to become sober. This was my story with alcohol; thankfully I was able to decide that I didn't want to go down that path any further and it's been 7 years now.
Others may spend their lives going in and out of addiction creating hell for the family. They may spend long periods sober, then something clicks and they're back to the addiction. You don't know what your BF is capable of yet.
Maybe when he meets your family things will ease off a bit for you. You don't have to defend him to them, but if you want peace tell them you're being slow and careful.