fights against his goal of becoming a merchant
'normally' it's an impossible dream, not to mention a downgrade in quality of life.
The family had no connection to a merchant (in this society, you basically get introduced to works via your social connections) wasn't educate enough to teach him how to read or write (not to mention other details that a poor family wouldn't care about, like
table manner) and didn't have the money to support him in pursuing such career (the siblings wouldn't need to fight over food if they've got enough money to fully feed them all)
Not to mention Lutz's original dream was to be wandering merchant/peddler. Go read the chapter when they first met Benno on why it's not really a good life to aim for.
It's like your child come in one day and go "I wanna cut off this family and go live on the street", imagine what kind of horrible parent would just go 'sure, we strangers now, door's that way'
Of course, Lutz's situation was not normal because Myne.
She taught him how to read/write/calculate much faster than typical children would get to learn, and he's a normal kid under 7 years old with some determination.
Her plant paper got them the apprenticeship and funds.
etc
But of course Lutz and Myne aren't explaining all this abnormal details to the family, so there's a big misunderstandings between them.
Like in this chapter, his mom say Lutz doesn't know how to read and write, but he actually do by this point.