Wow, Sharon, you mean you didn't study and memorize Delta's 70 page Contract of Carriage? LOL
https://www.delta.com/content/dam/delta-www/pdfs/legal/contract_of_carriage_intl.pdf
I think Page 29 is what legally describes what happened to you:
3) Failure to Occupy Space If the passenger fails to occupy space which has been reserved for him on a flight of any carrier and such carrier fails to receive notice of the cancellation of such reservation prior to the departure of such flight, or if any carrier cancels the reservation of any passenger in accordance with paragraphs of this rule, such carrier will cancel all reservations held by such passenger on the flights of any carrier for continuing or return space, provided such carrier originally
reserved the space.
I'm sorry to hear this happened to you. I wouldn't expect rookie travelers to know this, but most seasoned travelers do. One reason airlines do this is to prevent people from trying to book cheaper fares on different routes where maybe the added connecting flight makes it cheaper. Say you want to fly from Philadelphia to Paris; there's a direct flight to Paris, but a flight from JFK that connects in Philly to the same plane that is $200 cheaper. Delta wants to prevent you from booking the cheaper flight then skipping the first leg. Also, of course, if you legitimately miss the first flight of a connection, you would probably miss the connecting flight, so it's more efficient for Delta to free up that seat for someone else.
I've actually done what they are trying to prevent to save the money, too. Last year, I needed a one-way flight from Helsinki to Amsterdam. It was about 90 Euros cheaper to add a return leg to Copenhagen instead of just booking the one-way. But because I was skipping out on the last flight not the first one, I got away with it. Technically, they may claim they can charge me after the fact for the higher fare, but in reality they don't.
I can imagine that Kayak wouldn't be on top of this, actually, and wouldn't expect them to notify you. This is one reason I prefer to book directly with the airlines unless I'm saving a ton of money by using some third party like Kayak: the middleman usually offers nothing but complications and higher fees to change a flight and can block legitimate communication between you and the airline.