"I don't make threats." The Doctor, from the seventh story "The Sensorites".
It's interesting watching the First Doctor in action. I've seen about the same amount of episodes of One and Two, but the First is in the lower rung of my favorites out of the original run. Perhaps it's because he looked so old in my eyes, which of course is all relative. Now that I'm getting to watch more of his episodes and seeing how the Doctor's lore has been expounded upon in the new series, his comments like that stand out a lot more than they would have even ten years ago. It's kind of fun.
It's also good to keep in mind the original run of the show had now idea what was going to happen from story to story. The writers were very wise to leave the whole origin of the Doctor very vague at first, since that allowed them to add stuff to the mythos, just as they have ever since then. I do know the Ninth Doctor mentioned having a family, but has Susan's parentage ever been explained?
I don't think it needs to be, since then it gives fans something to speculate upon, much like the Third Doctor's inexplicable forearm tattoo.