Why does Smirnov challenge Mrs. Popova to a duel?

In Popova's absence, Smirnov rants and raves about how much of a soft touch he is to the people who owe him money. Well, from now on, it's no more Mr. Nice Guy; Smirnov's determined that Popova shall pay back the money that he loaned to her late husband. In fact, he's so determined that he's resolved not to leave Popova's house until she gives him what she owes.
But Popova won't play ball. She soon gets into (another) heated argument with Smirnov, during which she calls him all kinds of names, such as boor, monster, and of course, bear. Smirnov is absolutely shocked that Popova would have the nerve to insult him like this when she's the one who owes him money. He angrily insists that Popova will pay for her insults and that if she wants equality of rights then she will certainly get it. So he challenges her to a duel, which, to Smirnov's surprise, she accepts.