Browser addons can effectively create a new browser
(Certainly this is the case for me with my extensions. Adding gestures to Firefox significantly changes the UI I experience, while NoScript and other screening tools give me a much different and more pleasant view of the web.)
The direct consequence of this is that in many cases, people's core addons are not optional. If your addons stop working, what you wind up with is effectively a different browser; its UI is different, its behavior is different. This means that from a user's perspective, breaking addons can be the same as breaking the browser. Regardless of the technical details about what happened, you wind up in a browser that doesn't work right, one that no longer behaves the way it used to.
(A corollary is that once your browser is broken, you may well have no particular reason to stay with the underlying base it was built on. Humans being humans, you are probably much more likely to feel angry that your browser has been broken and switch to a browser from some other people.)
This is of course not the case for all addons or all people. Some addons have too small an effect, and not everyone will do much with addons that can have major effects on the UI or the browsing experience. But even small addons may have big effects for some people; if you use an addon that tweaks a site that you use all the time in a way that strongly affects your use of the site, you've kind of got a different browser. Certainly losing the addon would significantly change your experience even though that one site is only a small part of the web. I'm sure there are people using extensions related to the big time-consuming social websites who fall into this category.
(If you install a gestures extension but rarely use gestures, or install NoScript but whitelist almost everything you run into, you're not really changing your browsing experience much from the baseline browser.)