I've a question about Federal and State Taxes

I'm trying to find this out for our son.
He been working at a store 2 days a week
for over a year.

The old owners took federal and state taxes out.

Than a new owner took over and she was taking 
federal and state taxes out. But the last 4 months
she has taken Federal or state taxes out. 

My questions is should she be taken these taxes out.
She told my son no because he low income and he
has no depended. My other questions is wont my son
have to pay these taxes himself?

Thank you

Paying credit card debit off. Side hustles.
Saving money,coupons.
Bonnie Squires

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