Here Sesshomaru sees Inuyasha as a victim of their father's actions, so when his mother died, he decided to look after him, even if he's half-human, it's not like he chose to born like this. Then he took care of him the same way he does with Rin and Kohaku. Because of this, they end up getting a more friendly relationship.
(Please, click on the image to see with a less worse quality 🫠)
[ID: Shadow the Hedgehog from Sonic the Hedgehog tugs at the skirt of a young black Maria Robotnik. They look down at Shadow, who has sparkles coming from his eyes, with a smile. \End description]