Strange looks a little proud of himself. A more modest man would point out the many factors that lead to Strange becoming a magician, starting with 'it might be part of a prophecy' and ending with 'no seriously, I've no idea why I suddenly could do magic in my late twenties.' Strange is not modest. So Strange is going to gloat a little.

"Well I did do magic for the King of England." Just because there were only two magicians in England. And the magic didn't really do anything. But he's gloating and preening right now so those things don't matter! "I suppose that makes me 'really good' by default."