His mother die due to overworking
Kouichi's mom died due to overworking to maintain him. If Kouichi sayed in Caius' world, his existence from the original world would be erased, so at first he thought that his mom would get to live since she wouldn't have to die for his sake. However, Caius told him that the universe will find a way to keep things with as little change as possible, so his mom would die anyways, even if Kouichi wasn't there, meaning that his mom would die for some random reason. Kouichi can't accept this because his mom literally sacrificed herself for him, if he wasn't there, her mom would just die for a random reason, making her hard work for her son and eventual death completely meaningless. Therefore, Kouichi decides to go back.
What actually happened to his mom?
A bit confuse..