Disclaimer: Naruto belongs to Masashi Kishimoto.
"'Men have forgotten this truth,' said the fox. 'But you must not forget it. You become responsible, forever, for what you have tamed.'"
-- Le Petit Prince, Antoine de Saint-Exupéry
Konoha has many strong children, because Konoha takes responsibility for them. In a place where the focal point of the village is the ninja academy, and the strong clans are not merchant or samurai families but shinobi, and other countries besides their own pass dangerous missions to the ninjas that the village produces, there will always be a number of children who have lost family members, parents, or have been orphaned entirely. They are typically from shinobi families, but not always; and so the all the people of Konoha, villager and ninja, have a long-standing agreement to look after these children. There is no orphanage for Konoha--the orphans and any others who for some reason cannot be supported by the remnants of their clans are placed into other families. Even the tainted or unwanted ones are cared for.
Sasuke and Naruto were examples of that.
After it was discovered that Sasuke had left the hospital without telling anyone, and he was found within his family's compound, sitting beside the pond and soaking wet, it was decided that he needed to be put into a family that same night.
This was a problematic decision, since there was paperwork to go through and he was supposed to decide whether he wanted to be placed in a particular home or not. Also, since Sasuke came from an important shinobi clan within the village, it would have made sense for him to be placed within another ninja family. But as the majority of the shinobi were occupied with either hunting down Itachi or finding suitable people to replace the bulk of Konoha's wiped-out police force, there hadn't been time for any of the distinct families to look into taking him in. So for a week, Sasuke was moved through three different households. Once things settled down slightly, he was finally placed with a permanent family.
It didn't go as easily as it might have, despite the fact that he was an Uchiha--Sasuke never spoke a word about what had happened that night, and for a few years there was the worry that Itachi would come back for him.
Itachi was assumed disowned, and the Uchiha estate and inheritance was left entirely to Sasuke. He only used it to pay for his enrollment in the academy, until several days after he turned ten.
By that point, Sasuke decided that he was capable of cooking for himself and keeping up with the rent and bills of an apartment on top of training for hours, so he formally thanked his foster family for the past four years and demanded to be allowed to live on his own. There had been objections at first, both from the family and from a few of his teachers at the academy, but a boy who had mastered the Uchiha's great fireball jutsu in a week knew how to be stubborn, and soon Sasuke moved into a small but elegant apartment near the academy and far from his former home.
There was no change in his grades that reflected his move and independence, and eventually his teachers decided he was fine and there was no need to continue questioning his motives. Sasuke avoided seeing his foster family whenever possible, even in something as small as a casual meeting on the street, even after he had graduated and been set in a genin team. There are some things that are hard to be reminded of.
As for Naruto, he was really more of an exception than an example. He had nearly been killed at birth.
After the fox-demon was sealed, most of the villagers and no small number of the shinobi simply wanted to kill its vessel. But without the fourth Hokage to clarify, there was a confusion of whether the death of the vessel would mean the death of the demon, or if it would simply free it again--and this time with no one capable of sealing it away. So Naruto was suffered to live.
Very few people wanted to bring the fox-demon's vessel into their households, but since Naruto had been created as the equivalent of an infant, he couldn't possibly be left on his own. He was placed under the third Hokage's care until he was a toddler, to guarantee that no trouble with the seal would suddenly break out; and after that he was moved from household to household for a few years.
He was brought back to the Hokage when his current foster family reported that he was insisting on being allowed to enter the academy.
No one had expected or even entertained the thought of Naruto becoming a ninja, so his demand was surprising. It was also disturbing, because the work was blatantly dangerous and the village was still unsure whether his death would mean the equal death or the release of the fox-demon. When Naruto absolutely demanded to enter the academy and it became clear that he wasn't going to change his mind, a council composed of all the anbu, jounin, and chuunin was held to debate the issue.
The discussion dragged on for nearly two days, but finally the third Hokage said that he had faith in the fourth's work and that, if the teachers of the academy would accept it, Naruto might as well be allowed to join. After all, just because he had a desire to be a ninja didn't mean he had the skill to pass the exams--he might never graduate, or he might drop out in frustration, and then the whole discussion would be moot.
(Naruto had already decided he was going to be Hokage by then, but he hadn't started telling people yet.)
When he entered the academy, both of Naruto's current foster parents had their store to run and didn't attend the opening ceremony. Sasuke and Naruto's places were on opposite sides of the lines, and neither of them saw the other.
Three years later, Naruto had gone through almost every family that would foster him twice. He had stayed with the Ichiraku family longer than the others, mainly because he frequented their ramen diner so often that they had grown able to look at him and not immediately see the fox-demon's vessel; and for a long time they were the only villagers that he got along with. But even they weren't willing to take him in a third time, since he was such a troublemaker; and soon after Naruto turned nine it was decided that he was old enough to live on his own.
Since he had no family, and his training for the academy took up much of the time that he would have been able to hold a steady part-time job, the Hokage found Naruto a small apartment and set him up with an allowance that would pay for food, rent, and basic necessities.
He had a bad habit of forgetting about or losing his bills, so he got yelled at by a lot of creditors over the next three years. Eventually Iruka stepped in and taught Naruto how to do small but important things like filing bank statements and bills so that they could be easily found, and slowly the amount of times that he got stalked by irritable creditors per month decreased.
Though Naruto's acceptance within the ninja ranks grew rapidly after his participation in the chuunin exam, he still had trouble with the normal people of the village. But things started to grow better, as more than a decade passed and the adults began to be more comfortable in his presence and less reminded of the nine-tailed fox that had ruined so much, and as children his own age realized they couldn't think of why, exactly, they disliked him, except maybe for his personality.
The respect Sasuke had garnered among the shinobi took a long time to fail, even after it became widely known that he had defected to the Sound and the genin team sent to retrieve him came back with two members critically damaged. It wasn't until Kakashi would not speak about him to anyone but the fifth Hokage, Sakura, and Naruto that the other shinobi no longer brought up the Uchiha clan at all.
The third Hokage had never had a chance to tell anyone that he suspected Naruto had learned how to tap into the nine-tails's chakra, and thus must have found a way to converse with the demon. Jiraiya felt no need to tell anyone that he knew it.
Kakashi talked to no one about Sasuke's curse seal who didn't ask him about it first, and he neglected to ever mention that he knew Sasuke had enough willpower to activate its power and then force it back. He hadn't seen a reason to bring that detail up, even before Sasuke left--either Sasuke would listen to his warning about the chidori, or he wouldn't, and Kakashi couldn't force the boy to do one or the other.
No one could force Sasuke to do anything, except Itachi. It was the same way that no one could force Naruto to do anything, except any person he made a promise to.
There had been no deliberate motive to Sasuke and Naruto being placed in the same genin team, apart from a fate that could see months into the future. To anyone who had looked at them with only the present to judge by, they had nothing in common.
But they were examples, each in their own way, of the responsibility that Konoha accepted for its orphans.
And though they took different paths reflecting their lives, Sasuke and Naruto were also two of the village's strongest children.