OK, so it was a little abrupt, but there was no harm done...
From that hurried grab on, Aragorn treats Frodo and the other hobbits with respect and grace. He is a classy leader in his rough clothes. The best kind... He talks to them as equals, addresses them as "gentlemen" (as opposed to little ones). While leading he is indeed serving.
One of the quibbles I have with Tolkien in this part of the dialogue is where Aragorn whines that "I hoped you would take t me for my own sake. A hunted man sometimes wearies of distrust and longs for friendship"... Pulease! Everybody hug your lonely Ranger today!
I can see a good reason for Aragorn to do this, as distasteful as it seems. After seeing the little "show" put on in the common room, Aragorn probably had a vision of the entire enterprise failing right on the spot.
He had to impress on Frodo that not only was Frodo's life at stake, but the fate of all the free peoples, too. With stakes that high, a good, healthy shove would not be out of place as a way of emphasizing the point. It certainly got Frodo's attention.