Diapers contain SAP, that swells as it absorbs water. It can swell dozens or hundreds of times its original size.
When you flush even a wet diaper, SOME of that padding is still going to be dry. So assuming you rolled it up to fit down the toilet, it's going to take a minute or so for the water around it in the pipe to get to the remaining dry SAP and make it swell. Wherever the diaper is in the pipe at that time, it will probably try to double its size, with all the water available to it now. and that plugs the pipe. Or at least makes it more likely to get caught in a bend in the pipe and get stuck there.
The idiot that flushed the diaper in my previous post didn't just slow the drain by getting the diaper caught in a bend, it completely plugged the line. When we tried to plunge the line, it actually ended up breaking several of the sewer pipe seals between the toilet and the diaper, causing the pipes to start dripping at the joints.
So the diaper doesn't really "damage the pipes", but it renders them non-functional, and you have to have them serviced (lines cleared) which is inconvenient, expensive, and often messy.
I once had a squirrel crawl down the sewer stack vent pipe on my house, and finally climb up into the gooseneck below my toilet before he finally got stuck, died, and swelled up. It took plumbers over two hours to remove my toilet and extract it. Fortunately they were finally able to hook it under the jaw with a bent coat hanger and pull it up out of the hole where the toilet was. That was a $280 squirrel, and I shudder to think of how much more it would have cost if they had needed to disassemble my sewer line to get it out. Now I have a mesh grill over my sewer stack on my house, as does my neighbor.