I don't understand lia(n) vs. sia(n)...?
La feliĉa kuiristo ŝatas lian profesion. (The happy cook likes his (someone else's) profession.)
La feliĉa kuiristo ŝatas sian profesion. (The happy cook likes his (own) profession.)
Anyway it should take both answers as correct
No, that would result in a lot of learners not understanding when to use sia, in 90% of times the translation from English to Esperanto would be sia as you're usually talking about his/her own something.
True, except this sentence doesn't give enough context to determine whether lian or sian would be correct, so they both should be accepted.
Although quite possible to like someone else's profession, it would be quite uncommon to phrase it that way way [with his/her/their] in English.
I don't understand why is not correct "La feliĉa kuiristo ŝatas tre multe lian profesiono."
Lian is because kuiristo could be neutral gender, lian is for he (his).
Sian is gender-neutral. It's reflexive and means "the cook's own..." You're thinking of "ŝian," her.