AIBU to hate it when people answer the phone and then say they are too busy to talk to your right now.

[opinionatedfreak]

If you can't talk to me just let my call go to voicemail.

I'm talking primarily about personal calls. I'd much rather leave a message and be called back later when there is time to talk rather than be told that my call isn't important enough!!

On the other side and from a different angle I'm a HCP and people answering their phone during consultations is a real bugbear. It happens multiple times a day.

Put your phone on silent and if you forget do so when it rings. Don't answer it to tell the caller that you are seeing the HCP and can't talk.

I get

If you answer you can quickly agree a good call back time.
Otherwise you end up playing answerphone tag.

But not if in the middle of a formal appointment such as health care, or if at front of supermarket queue.

it doesn’t take anywhere near 2 minutes to say ‘I’m in an appointment, I’ll call you back’

But apart from that YANBU

I think you are conflating 2 scenarios -

1-in an appointment - I think most would agree that unless say the call was from a V vulnerable relative that could be an emergency then it is impolite to answer a call. I think you would agree that a V frail relative prone to serious illness in emergency, or wife in labour would trump your check up, but otherwise no.

2 - answering a call when you just don't have time to chat - there are some who take this as a slur for some reason that the person doesn't feel that they are important enough to talk to. There are others who answer, confirm it is not life or death and if they are busy assure the caller that they will call back, possibly agreeing a mutually convenient time. Personally see that answering the call and agreeing a time that suits everyone and you can give full attention to them as the most polite response.