There are no 'humane' ways to deal with a mouse infestation. If they're in your house, they will be getting through holes so small, you won't be able to even see some of them.
The least traumatic way of dealing with a mouse infestation is to do it quickly and efficiently.
It's natural for cats to deal with them - but whilst that's great fun for the cat, it's going to be much less so for the mouse. A kill trap is likely to be the fastest in the majority of situations, but can only deal with one mouse at a time and, thanks to their rate of reproduction, just two surviving by not taking the bait means you'll be back to square one within weeks. Glue traps are horrible.
Professionals putting down a professional grade poison will mean that the mice will die quickly (as they are getting a powerful/effective dosage) and it will deal with the entire nest at once, meaning there is less likelihood of having to do it repeatedly.
It's not nice for the mice, whatever way it happens. But I think he was sensible to go full nuclear on the infestation straight away, rather than try lots of different methods that are less effective and a lot crueller.
Even vegetarians need to eat food that hasn't been contaminated by mouse urine. Because if you have them in the loft, there is no way that they aren't also enjoying themselves in your kitchen overnight.
I don't think you are unreasonable in itself - it's not a pleasant thing to have to do, irrespective of whether you eat meat or not - but you are being unrealistic and he did what was right, even to the extent to taking responsibility for it away from you (as that means you aren't going to be in the position of realising there is nothing that can be done without killing them and feeling bad about making that decision). He did what needed to be done.