You need specific functionality. Every website contains text, photo and often also video. And there are plenty of fast, standard solutions for that. But what if the content of your website is the result of a logical calculation? Or comes from one or more data sources? This is the case more often than you think. Think of online counters, points of sale, calculation tools, data hubs, .... In that case, it is usually necessary to have a website made to measure.
You want to stand out. In the first place your custom website will make sure that you can be unique, that your website will not look like those of many others. This way you can make your brand stand out from the competition. The website will make you look professional and improve your credibility with potential customers.
You want to be able to respond quickly to new needs. If you have to respond to the reality of your business, your website must be able to grow with your company. Quickly providing extra functionality is more obvious in custom websites.