Because they are an expert in their field and the client, presumably, isn't? I can't imagine another field—hairdressing, construction, financial advice—where the client would reject the paid expert's viewpoint so readily and firmly.
The client here is just requesting specific content on their website, similar to someone requesting a granite countertop in their kitchen; that seems fine, even if its not particularly classy or aesthetically pleasing to the contractor.
To be clear, I would personally have a similar view to the author here. I'm just surprised that they think their opinion on the strategy side matters so much to their client!
There is also a general feeling that websites are primarily about design (rather than development) and that the design is aesthetic (rather than UI).
> I can't imagine another field—hairdressing, construction, financial advice
For financial advice, maybe not as readily, but it definitely happens pretty firmly. Lots of people have lost money taking risks they have been warned about. A lot during booms because of FOMO, and a lot because people do not even take advice in the first place.
People come to hairdressers with own ideas about how their hair should look like and reject hairdressers advice. In fact, hairdressers are not even trying to give you advice unless you explicitly ask for it. They sometimes makes mild suggestions and offers, but that is it.
Frankly, financial advisors are more likely to give advice designed to max out their bonuses rather then one good for you. You probably should firmly reject that financial product or flat tire insurance.