Being wise and proud he did not liked to explain his reasons to anyone. I put it there myself. For very good reasons. You asked me to find the fourteenth man for your expedition, and I chose Mr. Baggins. Just let any one say I chose the wrong man or the wrong house and you can stop at thirteen and have all the bad luck you like, or go back to digging coal.
Lets have no more argument.
I have chosen Mr. Baggins and that ought to be enough for all of you. If I say that he is a Burglar, a Burglar he is. or will be when the time comes. There is a lot more in him than you guess, and a deal more than he has any idea about himself. Now Bilbo, my boy, fetch a lamp, and let's have a little light at this. So, no one can tell for sure why he did that, but one can think, beyond the shadow of doubt that he 'sensed' that Bilbo is a 'man' for the job.