One important thing about a website, any website, is that you should be able to tell where users click and how often. The concept is the same as the electronic price scanners in the supermarket.
If people in the grocery store suddenly start buying a certain brand of coffee, the manager needs to order more coffee to fulfill the demand. Price scanners allow him to do that, quickly, easily and efficiently. Often the manager doesn't even need to do anything more than print out the report from the computer.
The same thing goes for websites. Webmasters need to know what people are looking at so he can make his site better. If people are clicking on certain areas of the site, the webmaster will probably want to put more content on the site that people are interested in. Furthermore, when Google's web crawlers come to your website, you'll want them to gather the right information so that you can be ranked higher in their databases. The better your ranking on the search engines, the more people come to your site.
The problem with Flash is that you can not easily track the user's activities and the web crawlers can not easily index your site. Once your usage log records that you served a Flash file, it hits a dead end. Once the Googlebot hits your Flash-based site, it stops indexing. Neither you nor Googlebot have an easy way to know what pages are most popular or relevant. Yes, there are ways to work around the problem but why should you? HTML, JavaScript and StyleSheets were designed for the purpose. Every click and every file are tracked.
So, why would you spend a lot of time building a website, paying for server space and bandwidth but set up a website which does not allow you to know whether your money is well spent?
I'm not talking about "Big Brother" kind of data gathering. I'm talking about aggregate data. For example, you might collect statistics on how many people click on an icon of a digital camera versus the number of clicks on a vintage Rolleiflex. If 50 people click on the digital camera but 250 people click on the Rolleiflex, you would probably like to know that. Wouldn't you? And, knowing that, wouldn't you be thinking about redesigning your website to favor the things that your visitors want to see?
With Flash, it's not as easy to do that. That is, among all the other reasons, why Flash is bad...