"It's not being humble. It's simply bringing you up to speed on what I plan to do." Because he just had this fight with Yuya, he wants to make certain Childermass is on the same page. Granted, he suspects Childermass knew this already but then again, he suspected Yuya knew it already as well and look how that ended.

"You think too little of yourself. People will listen to you—and not just because you have the book of the Raven King. They will listen to you because you have experience. They may scoff at you at first, but the moment you melt into the shadows or knock off their hat with a gust of wind, any true magician will sit down and listen to you. Whether people like it or not, magic was given to all of England."

And if they persist in trying to limit magic based on class, race, gender, and the like...well, Strange was going to return to England at some point. Perhaps he still had a little bit of weight and reputation that he could throw around to change that.