I love Heydon's breakdown of why "accessible" =/= "good". To paraphrase: accessibility is about removing barriers that would prevent people from using your site, but if the content is crap or the functionality is confusing then all you're doing is letting more people suffer a bad experience. Inclusive design seeks to remedy that:

Access is important, but inclusion is bigger than access. Inclusive design means making something valuable, not just accessible, to as many people as we can.

He also makes a good point on why inclusion is not the same as "a11y" + "UX":

In short, inclusive design means designing things for people who aren’t you, in your situation. In my experience, mainstream UX isn’t very good at that.

Inclusive design aims to make sure things work for people, not forgetting those with clinically recognized disabilities. A subtle, but not so subtle, difference.

As accessibility experts have been arguing for years, we're not talking about edge cases; inclusive design makes the argument that creating a better experience benefits everybody whilst having the neat side effect of also improving accessibility. It's a reframing of the age-old argument and that is better than simply keeping the old argument because it doesn't appear to be getting anywhere.

For instance, no matter what your cognitive or visual abilities are, small text presented with a stylised font on a low contrast background will be hard to read. Instead, using high contrast ratios with simple typefaces and supporting functionality like pinch-to-zoom makes your site more inclusive and accessible all at once.

Then, finally, there's this neat summary of why we should use semantic HTML:

HTML is a toolkit for inclusion.