Our cat, an 6 years old male, just came back after 6 days missing.

We all been so happy to see him.. We just wonder: why he would leave home for so long?

He is neutered from little age
He is mostly an outdoor cat, having his "nest" on our coridor from where he can always go out whenever he wants.
He was fighting sometimes with neighbours cats or even with foxes coming sometimes in our garden.

We thought maybe he got trapped somewhere because he lost weight a lot.

But he is now shy and not asking much food, he doesn't stay too much round us like before, mostly in the garden or in front of the house. Very unusual for him.

The question is? Would it be possible to leave home if someone coming to our house quite rare (like our cleaner - coming once a week) or a cousin coming time to time to play tennis table? Would the cat leave home for few days if a stranger kicked him?

Cats do that, especially male ones. Just because they are neutered doesn't make them any less macho cat of the block.
My cats disappeared for months at times.

Definitely if they are mistreated they will leave for a long period or even for good. My son scared three of my cats off and they refuse to even come to me or in the house.

Tell visitors to kindly leave your cats alone.