On what grounds did Yosef reject their explanation?
Seforno: He insisted that they came to spy out the land, 1 and that their claim that they were brothers was a facade to justify such a large group of purchasers.
Oznayim la'Torah: Refer to 42:11:5:2. Yosef replied that, to the contrary, they had just repeated their first mistake by volunteering details of their families without having been asked.
Rashi, Ohr ha'Chayim: They entered through 10 different gates (Bereishis Rabah 91:6). Surely this was to see Ervas ha'Aretz!
Malbim: Indeed, you proved that you are not spies to see the attributes of another land. They were sent before you. You are spies sent to inspect the fortifications, soldiers and Ervas ha'Aretz, i.e. the easiest parts to capture! One sends 10 mighty men, so if they are caught, they can fight to save themselves!
Ha'amek Davar: Indeed, you were not spies beforehand. However, now that there is great hunger, people change their Midos. You came from your land to see Ervas ha'Aretz, and to fight afterwards!
QUESTIONS ON RASHI
Rashi writes: "But behold, you entered the city through ten [different] gates!" Why explain Yosef's words this way?
Gur Aryeh #1: Yosef had already accused them of being spies (42:9); it would seem that this verse does not add anything to the original accusation! Rashi therefore explains that he was responding to their defense - 'If you are brothers coming to buy food, as you say, you should have entered through one gate!'
Gur Aryeh #2: The words "Lo Ki" (Not so!) imply that Yosef had a certain claim (Ta'anas Bari) against them; Rashi tells us what it was.