In the book version of Revenge of the Sith Yoda and Obi wan are discussing what to do with Padmé's twins. Obi-Wan was telling Yoda that each one should take one of the children, that he would take Luke to Tatooine and train him and that Yoda should take Leia and train her.
Yoda immediately said "No. Jedi training is not the only way to hone their skills and strength in the Force." Obi-Wan was quite confused. Yoda said "Trust in the living force, we will."
He chose to trust that the Force would guide them along the proper path and train them unconsciously for whatever tasks they needed to learn when the time was right. Yoda had learned that the Jedi became too dogmatic in their approach to training Jedi, which in the long run is what did the damage.
This is proved in Episode IV, in Luke's exchange with his wing men during the Death Star trench run:
Luke: Biggs, Wedge, let's close it up. We're going in. We're going in full throttle.
Wedge: Right with you, boss.
Biggs: Luke, at that speed will you be able to pull out in time?
Luke: It'll be just like Beggar's Canyon back home.
Thus showing that what Yoda said was correct, that the Living force was guiding and training Luke through his childhood on Tatooine ("I used to bull's-eye womp rats in my
T-sixteen back home. They're not much bigger than two meters.") for the skills he would later use to serve the light side and help restore the Republic and peace to the galaxy.
Just as Leia was learning all her diplomatic skills that she would need to help hold the Rebellion and later the Republic together in the decades after the fall of the Empire. She also did become a very powerful Jedi later on in the expanded universe books as she realized that over and over again it was not really her diplomatic skills that kept saving the galaxy, but the Jedi. She realized that she was wasting her tremendous potential as she knew that she could be just as powerful as Luke and that having someone else on Luke's level, or even half of that, could make a crucial difference in defending the galaxy. So she eventually put aside everything else and focused solely on her Jedi training some 20+ years later, though she had been slowly training for the previous 15 years. She was basically at the level of an advanced padawan up until that time.
Thus, the Jedi learned that it was better to let life train each Jedi as the living Force willed, then when they were ready, the teacher would come. Later on when Luke started his own Jedi academy, he allowed, though didn't necessarily encourage, attachments, relationships and marriage, didn't force Jedi to start at a young age, unless they wanted to and allowed each person to serve the galaxy and the force in a wider variety of ways than only being a Jedi knight.