If I add a widget with the titles and the teasers of your posts on my website - technically - I'm not copying anything.

This is what syndication is for. I choose what to syndicate, to add value to my website. And you gain exposure from appearing on many different websites. That's why most publish just a teaser of each post and not the full body.

Again, I'm not arguing about what is right (or fair) and what is wrong. I'm just saying that the protocol has been developed for this use.