DONT EAT TUNA WHILE YOU'RE PREGNANT. Tuna are the big fish of the sea and because of this they end up having much more mercury in their meat. You don't want to hurt your unborn child for something as silly as enjoying a sandwich.ONT EAT TUNA WHILE YOU'RE PREGNANT. Tuna are the big fish of the sea and because of this they end up having much more mercury in their meat. You don't want to hurt your unborn child for something as silly as enjoying a sandwich.