When Gai and Kakashi met they were four years old and had just managed to break ten slats off the wooden fence that ran around the Konoha Ninja Academy grounds. They'd been fighting, whaling the hell out of each other with four-year-old fists and size two traning sandals. The altercation had quite the audience, half the Academy students - never mind the staff who ran out tear the two boys off each other as they crashed out into the street. Gai was yelling his head off in his loud and immensely impressive fashion; and true to his quiet form Kakashi wasn't making any noise at all. But when Gai manged to pin him in a headlock for half a second he could feel the growl stirring in the smaller boy's chest. Gai still doesn't remember what they were fighting about, just that it had been quite possibly one of the very best fights of his life and he sort of wishes the bruises hadn't faded.
They both got dragged into the Principal's office, and their parents were called while they sat stubbornly refusing to nurse their wounds. In short order Gai got a stern ticking off from his mother (Gai-kun, you musn't be such a hot-blooded nuisance!); Kakashi got an almost-worried snarl from his father (Kakashi, you aren't like other kids you could have killed that boy!) and the Academy Principal told them to apologize to one another.
What followed was, documentably, the first act of outright rebellion in either of their lives. It was also the first in a prolonged string of rebellious acts that wound up defining both their reputations - different as they would be - and later on it wouldn't be lost on either of them that they did it because of each other.
Neither of them would apologize.
Gai refused because he was in no way sorry he'd followed his impulses and fought with Kakashi. In fact, he was feeling immensely proud of himself and if nothing else Gai believed in his feelings.
Kakashi refused because, as he quietly and hesitantly pointed out to his glaring father, Gai had more than held his own and Kakashi had known he'd be able to when they started fighting in the first place.
Each of them recieved a none-too-gentle cuff around the ear and three weeks detention. Gai beamed at Kakashi the entire time because he'd found someone who considered him an equal. Kakashi gave him sidelong glances and wondered how anyone's teeth could be so shiny. Gai was hellbent on the two of them finding out who would have won their fight, and (because he was the curious sort) so was Kakashi. They were forbidden from fighting while they did their detention chores so they competed to see who could do them faster and better. By the time three weeks was up Kakashi had just beaten Gai in a race to finish cleaning the board dusters and they were both covered in chalk dust, sneezing violently, and officially tied six to six.
The link between them couldn't have been more clear: screw the war, screw the responsibility they were being made to take on, screw the killing skills they were here to learn, and screw the fact that even after three weeks they hadn't even introduced themselves properly yet.
An Eternal Rivalry was born