carers leave is there for medical care - and most workplaces would have a policy that requires a medical certificate to provide carers leave. it's like taking a sickie - there is documentation required

your partner should be checking on paternity leave/parental leave.

birth, unless it requires c/section, probably wouldn't require additional care - it's a natural process. yes, it's great to have someone to help you out, but it's not something that would warrant your partner taking "sick" time - if one of you is ill, yes, but i kinda agree that the process of birth doesn't warrant it

hopefully he can clear up the paternity/paternal leave thing though. my understanding is that most larger work places offer 2 weeks paternal leave - generally unpaid unless it's in their award/contract