They had problems because of their different mindsets/upbringings. ML was raised to be an emperor, and had the responsibilities of being one, while MC wanted a husband that only had her as his wife, which wasn't the norm in that time. They tried to work with it at the beginning, but the small problems added up, and MC ended up leaving. This woke ML up, and he started to try to understand MC's mindset, but didn't truly do so until he went to modern times.