>>719040813
He was tired of this cat and mouse game he's been playing with Carmelita. If he wanted to keep thieving he would've escaped the Vault with Bentley and gone back with the gang. He voluntarily gave it all up, even leaving his cane behind, the literal key to his family's riches and the only thing left of his father. Bentley also became the Thievious Raccoonus' successor.
Sly was done with thieving and passed the torch to Bentley. He had pulled off the greatest heist in his career and managed to get with the girl he loved.
Sly has tremendous respect for his family name, but at the same time knew it didn't define who he is (unlike Tsao for example)