What was wrong with the old one?

1. As previously mentioned, it was not mobile friendly. Phones make up most internet traffic, so you're actively making your website inaccessible to most people by not supporting that platform
2. The old website was built on outdated technologies and was not HTTPS compatible
3. It looked dated, and (as much as they shouldn't) people will make judgements about the quality of your service based on aesthetics. If they want to compete with other weather websites, which I think they should, they need to play the part
4. The old website had multiple usability issues (e.g. interactive target sizes, other things I list below, ...)

What does screen reader compatibility even mean? Whose screen? Mine? I use a lap top.

Screen reader. Like for blind people. Who need the screen read out to them. Verbally. By software. Whom the government should be considering while building digital services. See previous mention about "usability issues".

Who cares what the average user expects, it’s up to the smart people to set the standard

I'm glad you consider yourself among the smart people. I haven't worked with the designers on this particular project, but like most I've worked with before I would assume they're also reasonably intelligent. They'll understand, just like I'm sure you do, that a good interface is an intuitive one. We all have mental models of how we expect software to "feel"; how it should navigate, be structured, and just behave in general. Any time you break that model, you add friction as the user has to learn how your specific app behaves. Of course, there are sometimes good reasons to do so, but I would argue that the weather, which is generally considered a basic task, is not one of them. Therefore, updating their website to match common, modern, and well reasoned design patterns to make it more accessible to new users is reasonably justified.

That said, existing users of BoM already have a mental model of the website, and by updating it they're breaking it. They're essentially privileging the experience of new users and they should be careful to ensure the redesign is actually necessary. This is a trade off of all redesigns but, considering my previously mentioned issues with the old website, and their clear effort to maintain feature parity, I would argue that that is fair in this case.