No sense in both being tired

This is what my husband says to me. I’m a SAHM and don’t work. I was talking to my husband about getting up with the baby. Why he doesn’t get up with me sometimes. I hear about these husband’s who get up and grab the bottle and bring the baby to them. Especially those recovering from surgery. Or them switching off through the night. We never switch off. My husband said to me “well there’s no sense in both of us being tired”. I just don’t understand this. I asked him to explain and he said if he did that then we’d both be tired and one of us needs to be rested. Then what sense does it make for one of us to be exhausted all the time? If we were both tired than it would be fair. Only one person doing all the stuff and being exhausted seems unfair in comparison. Can someone help me better understand this?