Because this might be like his last chance to sign for a bigger team to compete for titles. Otherwise I don't think there would be many teams at his door after a point. He is aging day by day and he is already 29 now. Tottenham are in no condition to win any title now. They just maintain their same form every season. Joining the Champions League shouldn't be enough for a player like Kane. But if he doesn't mind not being able to win any title with his team then it's his choice.
I also thought that Harry Kane needed to play for another team to win a few trophies, but he became the top scorer in Tottenham history. He is probably the most important being after God at Tottenham. He may not believe he needs to go to another club and take on a new challenge. Being remembered as a Tottenham legend may be more important to him. He's going to have a really interesting career.