Hiccup punches Snotlout.
Race to the Edge S2E06
Not original clip. Twins were removed and the audio fixed to hide splice.
I think it needs to be pointed out that the action was not committed in malice or with the explicit intent to do harm to Snotlout simply for the sake of harming him. Snotlout flat-out told Hiccup to haul off and punch him after engaging him in a faux fight when Hiccup hadn't been aware of what was happening and had tried to walk away. Up until the point of the challenge Hiccup had been working to dodge Snotlout's swings and to avoid engaging in the scuffle. Hiccup only relents when his standing as future Chief is insulted and he's invited to do harm without any resistance. He's issued a challenge and chooses to accept.
His patience is already wearing thin because of Barf and Belch, and it's no secret that he and Snotlout don't exactly get along. Hiccup handles it fairly well, but he's constantly under a lot of stress as leader of the Riders and The Edge as well as the future Chief of Berk. He's been dealing with stress since he was young and has largely learned how to cope. But we do see him lose it every now and again in one way or another when the frustration gets the better of him. He's letting go of his calm demeanor and letting himself give in to his frustrations and indulge in doing a bit of harm.
Keeping in line with the above, prior to Hiccup hitting Snotlout, he directly insults Hiccup's standing as future Chief. He calls Hiccup a coward, which is essentially saying he's unfit for the role and will fill that role very poorly. We can see this verbal attack hit Hiccup when his expression changes. This is what really makes him angry.
Now, we as viewers have to remember that Stoick has been pushing Hiccup to learn and grow to be the next Chief of Berk. Hiccup is very much dead set against the idea right up until the end of the second film. He doesn't feel that he can live up to Stoick's or Berk's expectations of him as a leader and this is a huge source of stress for him throughout the franchise. When Snotlout calls him a coward, not only is he insulting Hiccup and his future role, he's also insulting the views and beliefs of Stoick and those who believe in him as a future leader. This may not have been his intention, nor may he have even realized what he was doing, but this is what was done.
On another note, Snotlout and Hiccup have always fought on petty much everything. Snotlout has a very large personality and ego and thinks very highly of himself. Hiccup, on the other hand, is largely self-depricating, self-conscious and fails to stand out in a lot of ways and prefers to keep it that way. They are polar opposites. Snotlout will fall into the general opinion of what a Viking is meant to be, while Hiccup embodied everything that had been seen as being wrong in a Viking. This leads to endless clashes between the two. There is a practically endless power struggle going on between them and it's frustrating for both parties. The difference in dealing with this frustration is while Snotlout is a very physical person and would prefer to pound on his problems, Hiccup is a much more passive person and would rather resolve things through diplomatic means. This often just leads to even more frustration between the two and they are often left in a stalemate or with one having to begrudgingly concede to the other
So, in this scene we see Snotlout not only catching Hiccup while he's stressed and irritable, but he's also hitting on some sensitive nerves. He's hitting all of the right buttons to get Hiccup just riled up enough for him to accept the challenge that has been issued. However, given Hiccup's history of seeking any non-violent solution to a problem that he can find, I don't think Snotlout really anticipated that Hiccup would actually punch him. Or, given Hiccup's stature, that if he did the resulting swing wouldn't have had any real power behind it. This scene shows Hiccup's personality and also shows he is a lot stronger than he lets on or even than he really knows himself, and while we often get to see this non-physically throughout the film and series, this example is a comic reminder that he's no pushover.
It's also worth noting, I think, that Hiccup makes a point to remind Snotlout that he his taking a swing is only because It was asked of him. Hiccup makes it clear to him and to the viewers that this action isn't him simply losing his cool, but more so that he's accepting the conditions and requests that have been offered along with the issued challenge. He's making it clear that hitting Snotlout was not his idea, nor his intention, and is absolving himself from any consequences in doing so. Snotlout is a constant source of irritation and torment for Hiccup and now we get to see him give some of it back to him. It's a very satisfying scene, as well a a very funny one. And aside from that we get the added bonus of all the under-the-surface stuff that goes along with it.