It is not necessary that he had authority over mom. But, he was likely responsible a lot for younger kid - maybe when she was not around or too tired or just in general. He might be babysitting too much basically and have to solve siblings issues parent would normally solve.

It has name in child psychology, through I can't recall the name now. But in general, altrough it makes older kid more responsible, it does harm him overall.

Note: it is different isue then chores and some help around the house. Kid won't be harmed by helping and working then, it is responsibility beyond kids age and having to grow.l too soon.