I am sorry to hear this, Laura!! I was afraid this was going to happen.
I don't mean any disrespect and if it sounds disrespectful, I apologize, but I do think that you humanize Max and the other dog a little too much. 9 out of 10 dogs will get aggressive when another dog enters their territory.
But it is funny that you say "it is not just my decision, this is his decision, too". My first words to the breeder when I was looking at Tuxedo, were, "Scooter is the one who has the last word". From there, I have learned that it is NOT the dog's decision and dogs are NOT our equal, we have to decide what is good for them. If we treat them as our equal and humanize them, it is a disaster in the making.
When Scooter and Tuxedo met for the first time, it was a disaster, they went at each other with a vengance. I was totally shocked! Scooter, my social butterfly who greeted EVERY dog at the dog park wiggling his butt, playing, running, who never got into a dog fight, who never fought back when other dogs picked on him, turned into a raging maniac. So I told the breeder that I couldn't do it and brought Tuxedo back. I told the breeder that Scooter just didn't like Tuxedo, I was looking for a playmate for Scooter and Scooter had spoken loud and clear.
However, I really liked Tuxedo, talked to the breeder again, read about how to introduce dogs, watched the shows about it and gave it another shot. This time around, I did not let them sniff each other or look at each other, took them both on a leash and for a 60 minute walk, one dog on each side. Well, it made all the difference.
Fast forward, now they are the biggest buddies, they sleep in a kennel together, they are almost joined together at the hip, Scooter goes where Tuxedo goes and vice versa. What I am trying to say, it rarely is all iddle sunshine when you introduce 2 dogs - puppy or adult, really doesn't matter.
Most dogs feel threatened when another dog enters their territory. It is up to the human (the pack leader) to make it clear to the dog that it is okay for the other dog to enter the territory and that that dog will be a member of the "pack". When we just leave it up to them, let them off the leash and let them at it, the original dog thinks the pack leader has gone for a nap and he/she needs to step up and defend the territory.
I am not trying to tell you what to do, I just think it would be a shame to give up so quickly. I know you don't have much time, but I do think it would be good for Max AND for you to have another dog. It may not look like it is any good but maybe you can give it at least this weekend.
Sorry this was so long-winded, I know what you are going through because I had the same thoughts. In retrospect, had I not had the breeder convince me to give it a second shot and give me another perspective, I would have missed out on one of the greatest dogs ever, Tuxedo!! And Scooter wouldn't have his beloved playmate.