He has some point of his stance thinking that trying a new one will stress him from familiarizing how the platform works. He never feels comfortable doing it and that sometimes happens to me. Every gambler has their choice and favorite gambling site which makes them prefer to stay using it rather than trying a new one even if they have a good offer.
It makes no sense and instead of doing this, better to let him choose what they prefer. We better respect his decision rather than forcing someone as this won't help but instead, this probably creates misunderstandings and blaming especially if he loses. Because it was not the offer but the place where he felt comfortable.