You would insist wrongly, then. There is a mass/energy duality involved in both "nuclear" and "chemical" reactions. Nuclear reactions are just more energetic, generally a million times more energetic, so the mass/energy loss is about a million times greater than chemical reactions.
But there is indeed a mass/energy conversion involved even in chemical reactions. But it is so small it is next to impossible to measure the mass change. For instance, if you lit a match in a sealed oxygen filled glass ball, and the only thing that could get out would be light and warmed (conducted) the weight(mass) would go down in proportion to the energy lost to light and heat. Of course, it is such a very very tiny amount no actual scale would note the difference.