It happens in the extend part.

This is it right here.

If you need a real-world example look at the original web browsers:

NCSA Mosaic (the very first web browser) fully supported what would be later known as HTTP verison .9 . There was universal compatibility because there was only one browser supporting HTTP. Later Netscape Navigator would come on the scene and add functionality that was not supported in Mosaic (like the tag for example), but nothing hugely breaking page views between the two browsers.

Fast forward to Internet Explorer v3, v4 and v5 where MS would not only show all the pages that the prior browsers would, but they EXTENDED by letting HTML still work without following all the same standards. It was easier to write pages for IE than it was to the specification. Then EXTENDED again by MS added ActiveX to web sites meaning now ONLY MS IE could display these pages, and for a time that meant only Windows computers could. This is the Extinguish part.

The "Extend" step gets adopted because its attractive to users.

Here's a non-computer analogy:

Lets say your current car get 25MPG. Now lets says that Shell come out with a gasoline that would let your same car go 40MPG with zero changes. Just buy Shell gas now at nearly the same price as anyone else's and you get significantly more range. Most people would do it. Moreover, Shell buys Honda and starts manufacturing cars designed to work on that same new Shell gas could go 60mpg with even more power! So when you go to buy your next car 5 years later after using the gas, you don't want to turn down 60MPG with more power. That Shell/Honda looks very attractive! All this time all the other gas stations have been going out of business because few people want to pay nearly the same amount for gasoline that only gets a fraction of the range. In the end, ONLY Shell gasoline is being sold, and nearly everyone drives a Shell/Honda to get the most benefit. This is Embrace, Extend, Extinguish.