Haven’t seen the episode but just saw this and, well, it’s pretty clear his mum told him this.
She was in the hospital and little Stiles was all alone in the room with her, as we know. She was probably having hallucinations and telling him all this weird stuff that didn’t make sense to him but he was used to that.
But then she had a moment of lucidity and asked him to come up onto her bed. She cuddled him and called him her big brave boy, told him how strong he was, how proud of him she was and would always be. She told him he was destined to do great things. She told him that his dad might have a little trouble for a little while once she was gone but that he’d pull through and look after him just as well as they did together.
But she also told him that his dad needed someone to look after him too because she knew he was going to have a hard time without her. She made him promise that he’d look after his father, that they’d look after each other, no matter what. She offered him her pinky and made her pinky swear that they’d take care of each other. Stiles nodded tears in his eyes and running down his cheeks.
By morning she was gone.
A lot happened over the years but when Stiles looked at his dad and saw him drinking himself to oblivion to try to get by, when he got involved in the supernatural, when his dad was taken to be sacrificed, he could still hear his mother’s words whispering through his head.
"Take care of each other, my precious little guy. Take care of your dad for me."
He hated how much he felt he’d failed on that.