Aragorn's political skills.

[Lalwendë]

He did have experience, but not political experience. As Thorongil and as Strider he was a soldier, so his experience was of the military kind. He was undergoing his learning, spending time in his own realm as an ordinary man, and giving service at the same time. He did not need political experience in such situations as his lineage was not made public. Once he started saying who he was, that was the time he would need political skills, as his statements and his status would be called into question. As Strider his actions did all the work for him, once he became Aragorn, his actions would need backing up with careful thought and behaviour.

Originally Posted by Formendacil

If Aragorn hadn't been so tired, he would have thought through what he was saying a little bit more, and simply put the sword down with a (very!) stern warning not to touch. But he was tired, so he didn't...

But wasn't he tired after the battle of the Pelennor Fields? Possibly even more tired, but in this situation he instead behaves wisely. This is because he has learned from what he almost did in Rohan. He followed Gandalf's advice and all that followed could only have been to his advantage; he demonstrated his leadership qualities at Helm's Deep and gained the respect of Theoden and his people, and this would have proved to him that he did the right thing in that situation. In between Helm's Deep and Pelennor, it is notable that Aragorn keeps very quiet at isengard, another difficult situation, where he seems simply to observe how Gandalf handles Saruman.