leaving baby at home

What age has everyone felt comfortable leaving baby at home with dad so that you could go out and run errands? My LO is 3 weeks and my BF is offended I won't leave him yet! He thinks I don't trust him. Which is not the case, however he only watches him so I can cook or clean as it is now. He seems to only want to watch him when it benefits him not to actually spend any time with our son. And the response from him about me not leaving him came about after a post on social media about how much I miss showering and apparently he received a few phone calls asking why he wasn't helping.