The scene in the manga strip about Canada's independence is interesting, because it can be agreed Alfred is acting in a childish way, being rude instead of congratulating Matthew like a person should considering such a great achievement.
Matthew rightfully snaps back, but his choice of words are a strange thing to say. Perhaps he feels stung by the fact the U.S. neither helped nor hindered Canadian efforts for complete independence from Britain (?).
Considering 'world's greatest show off' is in reference to the Revolutionary War, it's a bit of an unfair point to make.
Because unlike other wars mentioned throughout the series, the Revolution was one of the times Alfred was at his most serious, fighting a battle that caused bloodshed and loss on both sides, and broke a relationship so badly even now there are still cracks in it.
Which, in a way, gives Alfred somewhat a right to be angry, considering Arthur communicated with Matthew through diplomacy, giving him the rights of a self governing dominion, and eventually nationhood. And this probably stings to Alfred, who sees this as further cementing the fact that Arthur loves Matthew more and vice versa.
Alfred had went to Matthew probably expecting his brother to take his side in pushing back against England, with Matthew facing many of the same struggles himself, but instead was hit with the reality that Matthew was more loyal to Arthur, and had rather had stability than uncertainty.
Historically, The Quebec Act of 1774 helped secure the loyalty of French Canadians by guaranteeing their rights, which contributed to their decision to stay out of the conflict. So, this would probably be hurtful and upsetting that Matthew stayed on the sidelines with a safety net while Alfred had nothing to fall on but Arthur's kindness if something went wrong.
Probably a terrifying thought to him, he was a colony who could fail and be crushed economically and physically by an empire who had already showed what his real priorities were.
Again, Matthew being upset about them fighting is valid, but also a bit undermining considering the situation. AND Alfred had already spoken to Arthur, sending diplomats to and from England, only to be punished more for it. Diplomacy refused to work on either side.
Once again criticizing Alfred's way of trying to barge into Matthew's house unprompted, and giving Matthew points for standing his ground (though it was mostly just criticizing Alfred's food choices). But, Alfred wanting to speak with Arthur was not that difficult of a request, and despite Arthur being sick, he could have managed to tell Alfred to go and slam the door in his face himself.
Matthew was defending his home, but was also getting in between something that he was not apart of and already made clear he didn't want to be a part of, so hiding Arthur could have been seen by Alfred as another act of Matthew choosing Arthur over him again. (Especially when Matthew is aware of Arthur's slight favoritism during this period of time).
