She was happy to check and only asked to clarify what shop he was going to
It was an unnecessary check.
He was obviously rude and patronising but there is a certain demographic of women who consider that men are a bit useless and "what would he do without me?"
My mother was one. Her partner's incompetence/inability to tidy up after himself/cook/use the washing machine was put down to the fact that, well men are actually just a bit useless. It's exactly the sort of thing she would have said, with a smile and an eyeroll, to highlight his incompetencies to an audience.
And when he did take resonsibility for something, householdwise, she would fuss and bussle and micromanage because he "couldn't be trusted" to do it on his own. "You know what men are like..."
She wanted to know which shop he was going to and advising him that 5 minutes would be enough.
He might have had a letter to post; a cigarette to smoke; fuel to put in the car; giving himself enough time to get it done...
The way he spoke to her was appalling but I think if I'd said I was going to the shop and I'd be 15 mins, I wouldn't appreciate someone else checking the details and correcting me. It's just not that important,
He was saying he'd take more than 15 minutes to do a five minute job, which caused her to wonder
But why though? Did it really matter? So what if he was back sooner than he expected? So what if he just took his time and ambled around for a bit. So what?
If the exchange happened exactly as the OP said, the woman should have just said, "ok". If a husband had asked what shop and corrected the time expectation, he'd be accused of being controlling.