What is the word that we use to call a father who is the main earner in the family?

Solution 1:

You can call such a person (m/f) a breadwinner:

a person who earns money to support a family

(source: Merriam-Webster)

Solution 2:

You can also use the idiomatic expression: he who brings home the bacon:

  • to earn money to live on:

    • If Jo is at home looking after the children, someone needs to bring home the bacon.

(Cambridge Dictionary of American Idioms)