"It's Okay, I don't tell most people. I haven't even told her. She doesn't need to know who I am yet. She's done quite well for herself over the last thirty years."

Red truly does believe that. He already brought enough chaos into Elizabeth's life. Knowing that he's her father for sure, would turn everything even more sideways than it already was. He knows, she'll find out eventually, but now isn't the time.