I would think that honesty is the best policy when applying for the actual visa. I never would have encouraged my boyfriend to lie during that process had we been together when he applied, eek! (He didn't btw.) Probably should have clarified that, but I just wanted to share what I know for a fact several friends have done. The advice people who have had to apply will give you and the advice Americans will give you is often different. BF needs to renew it soon and if that gets approved it's for 10 years, yay. Fingers crossed. I just asked him--This time he's going to get a letter from the company that contracts him to say that he's been working with them for years, blah blah, and that at some point he might need to take a technical course in the U.S. for his job. This is true.
Still, landing in the U.S., or anywhere for that matter, and passing through immigrations is another thing. If they ask him why he's in the U.S. and he says tourism, it is the truth, or at least the truth without superfluous information. I just wouldn't bring up the relationship before they do; it is asking for trouble. If they bring it up, then by all means be honest. I learned my lesson the hard way that if I tell the whole story upon arriving to wherever my boyfriend is (Colombia or Argentina), they peg me as a gringa drug mule due to my age, solo travel status, and zillions of stamps/extra pages in my passport. Citing my boyfriend as my primary reason for travel right off the bat without even mentioning his nationality got me sent to another line to be x-rayed with all the other potential mulas in three different airports, and even at Ezeiza at this point gets me a lot more questions and hassle due to all the time I spent as a permatourist. When I say I am just in the country to visit I don't get trouble, so that's what I do now. He, on the other hand, has never mentioned me at immigrations because they never asked, and as a result has had fairly easy breezy experiences in the Houston and Miami airports, the most stressful part being that this questioning was done in English. They don't care whether you need to make a connecting flight or not, and they take their sweet time.
One more thing-- Don't assume that you living in Argentina for 10 years will make a difference, even if you have residency. They assume that everyone wants to live and work in the U.S., and it is the applicant's job to prove otherwise. Having an American girlfriend will probably work against him no matter what. Of course you must be dying to return to the land of the free and the home of the brave after so much time in the icky third world, dragging your foreign boyfriend with you, they will probably assume.
But if he has enough $$ and a solid job, that should be enough to counteract the GF thing. Also, he is Argentine and lucky for you and him they have it much easier than many other nationalities. Good luck and enjoy your trip. I'm sure he'll be fine.