Why is it important for a website to be accessible?

The more accessible, the larger your audience.

No two computers (or users for that matter) are alike. Settings, software, and hardware vary from system to system. Also the skills of your potential users will vary as will their disabilities, if any.

You want your website to be easily readable and navigated for less experienced users, attractive and appealing to experienced users, and easily accessible for screen readers for those who have disabilities. The larger the audience you can provide for, the more response you will have to your website.

Not only are you looking for that initial view from a new user, but it is important to be able to lure them back time and time again. A website that is not easily accessible for certain users, will leave them frustrated and thus no return.

On top of that, you have various browsers, both on computers and now on mobile devices, that you need to be able to reach. Each device or computer has their own hardware to work off of that determines what can be processed.

So really you need to decide. Is it more important to reach only your target audience, or is it more important to reach the largest audience as possible. It depends on your goal you need to accomplish with the website you are creating. But when it comes down to it, more accessibility means a better (and happier) response.