1. The virtue of the American people and their institutions: The whole world is being carved up by the Great Powers, and America is the most free and enlightened people. Better us than some truly repressive power using them as say, resource extraction serfs, or whatever
2. The mission to spread these institutions, thereby redeeming and remaking the world in the image of the United States: Japan is gonna have to make a leap forward to compete in the world sooner or later. It's better to have another country with republican traditions and appreciation of free trade than to risk Japan self-actualizing as another absolutist state, prone to ally with absolutist states against republican states and interests. Whether they like it or not right now, it's risky to all the free peoples in the world should another enemy nation arise
3. The destiny under God to do this work: America has the most enlightened religious tradition and understanding of secularism, Japan needs to move away from the influence of a state religion, or worse still, potentially taking after a Papist nation

Contemporary officials in the United States government would probably not agree that they had "forced" Japan to open up to Western trade. They had forcefully demanded a negotiation. But (to their thinking) the outcome of the negotiation was a mutually beneficial treaty. Further they might note that the negotiation had not been "forced" by American commercial hunger, but rather by the need to address Japan's longstanding ill treatment of American sailors.

Whaling was a major American industry at the time. One of the primary whaling grounds of the 1850's was in the Sea of Okhotsk, adjacent to the Japanese Island of Hokkaido. Japan routinely refused assistance to American ships in distress near its shores, and had even occasionally imprisoned stranded American sailors. This treatment violated commonly held international obligations of the day, and provided all the ethical justification an American official might need to justify the Perry mission. Indeed, this was one of the main points called out in the letter from U.S. President Fillmore to the Japanese emperor.

Obviously there were self-serving motivations as well (i.e. potential for profit, strategic advantage over America's Pacific rivals, a need for Pacific coaling stations). But it was also believed that Japan would benefit mightily from trade with the United States, whether they realized this beforehand or not. American officials did not view this as such a one-sided arrangement, and therefore did not see the need to justify it as such.

It's somewhat insightful to review the justification presented in the letter from President Fillmore delivered by Commodore Perry. As summarized in the letter itself: "These are the only objects [of the Perry mission to Japan]: friendship, commerce, a supply of coal and provisions, and protection for our shipwrecked people."

Rather than speculate, this letter provides a decent picture of how American officials actually justified the mission at the time:

• Friendship: no ethical justification needed
• Commerce: mutually beneficial - a win/win!
• Coaling stations: which America will pay for - another win/win!
• Stop abusing our shipwrecked sailors: a minimum expectation of every civilized nation, not subject to any individual nation's preference.

Some sources for deeper information:

A book looking at the Perry mission from both American and Japanese perspectives: Yankees in the Land of the Gods: Commodore Perry and the Opening of Japan

Commodore Perry's own account: Narrative of the Expedition to the China Seas and Japan