The image quality for business cards is higher than average. They will need to compress the image if it doesn't have enough dpi. Hence, why he wanted it to be bigger. Just trying to change with size on your computer doesn't change the dpi.
The larger the image the finer the detail when it's reduced to fit the card.
It might come out ok if the image is the same size as the card but that depends on the printing process ink jet or scanner print, lithograph or photo print, etc. Ideally you should have an image that is at least 25% larger than the one you want to print especially if there is any text as well. I'm sure the guy is not trying to rip you off.. he's the one who's been doing it for years so trust the professional (or gifted amateur lol). If you're in doubt and want a large number of cards done ask for samples first before you decide, will probably save money in the long run.