Jiro's childhood
We barely understand that Jiro's Father sent him away when he was a young boy of (7)?.
We hear that his Father was probably an alcoholic.
Do we know why both of his parents kicked him out of the house at that young age?
His father didn't send him away. It was his mother. His father was an alcoholic who left home when Jiro was seven. His mother sent Jiro out to work when he was nine. The documentary didn't explain clearly, but he left to become an apprentice, which was normal during his time. As an apprentice at that age, he'll have lived at his employer's place or a local boarding house. During his time, the age range for an apprentice was between 6 and 14. It depends on which job.
My grandfather left home when he was 11 to work as an apprentice (his older brother left at 10). He stayed at a local boarding house until he could afford to marry my grandmother. Like Jiro, my grandfather didn't understand why should my dad and his siblings graduate at 18 when they could work as soon as they were legally allowed to leave school (6 or 11, depending on prefecture), but my grandmother insisted on them graduating for university. She got her way. :D