Whereas Harry is acutely aware that he's twice Eggsy's age and in face old enough to be his father and then some. Which... is not entirely an issue, Harry is aware that he can probably keep up with someone younger than he is.

"No, you have far more class than that, I'm aware. It would still be highly inadvisable. I'm your mentor, I have a position of power over you. Plus, I'm older than your father, whom I was also a mentor to." He can't bring himself to reject Eggsy, it would be a lie, such a lie, but maybe a bit of cold reality will help the boy.