The formation of the Genin Teams didn't have such a noble principle as one might think.
Officially, they were assembled for security and strategy. The planning was more effective with all the shinobi properly distributed, each team with significant strengths and weakness. That was the pragmatic principle behing the genin teams.
They were assembled early on, to new ninjas fresh out out the academy. These kids, who had been through school together, were now a part of their own little team. Their own little word. The peopley they would literally spend the rest of their lives with, who would be responsible for their life and death on multiple occasions. They would eat, sleep, bathe with them. They would share a lot more than they wanted to share, be completly vulnerable and dependent on eachother.
Talk about an emotional prison sentence.
No, the formation of the Genin Teams had much darker purposes than one could suppose. They picked them young, when their emotional bonds started to form. For many weeks, these kids would have nothing but their partners', they would be forced away from their parents', for the sake of some warrior notion of adulthood.
These bonds they form, they're not acidental. The love-hate relationship, the companionship, the competition, the love triangles : all part of living and breathing by and for a team. The village wants them all connected, not by duty or honour, but by love and friendship. Not because such feelings are more noble, but because they are more effective.
Just watch a mother die to protect her infant, a best friend acting as a human shield, a brother sacrificing himself for a sister. The spirit that hangs on, because someone they love is on the line.
And not only someone you love, but someone you've spent your entire childhood with, who as been with you through thick and thin. Someone you admire, someone you want to be recognized by. Someone who loves you back, with the same mix of friendship and admiration.
The bonds are eternal and strong. But also, even if just for a bit, artificial.
After all, they pick them young.