Your friend is absolutely right. I think he might have explained it further. I will put it close to the layman terms here. Neutrons are made up of three fundamental particle known as quarks. Two down quarks and one up quark (two stable form of quarks). When the charges of these three quarks are added up, one will get the net charge as zero. Which proves that the neutrons have zero ‘net’ charge. Add it up and check for yourself.