The "Tables are Harmful" club largely came from the crew who thinks HTML carries lots of semantics and that if you don't use the Blessed Tags that carry those semantics you're doing Bad Design.
The rational evidence in favor of this claim has always been weak. The "div" tag basically finished it off. The people who use HTML "semantically" have always been dwarfed by the people just making it look good on the screen, and the number of applications that use those semantics has always been small and on the fringe for something so putatively important.
However, the idea persists to this day despite its near complete failure to pay off significantly in nearly twenty years, and I'm sure someone will angrily reply to this and list the incredibly useful semantic HTML features that they and fifteen other people have found to be just incredible. Perhaps we'll also get the traditional citation of the Google info boxes, which have nothing to do with the semantic web and everything to do with Google throwing a crapton of machine learning and humans at the problem of parsing distinctly non-semantic HTML until they cracked the problem.
(An honorable mention to screen readers, which sorta do benefit, but still nowhere near as much as you might casually expect.)
Today the reason not to use tables is more just that it's inconvenient to do things like have a mobile and desktop layout. I believe they've got all the tools nowadays to tear into a table-based layout, break the tables apart, and treat it like any other CSS-styled content, but that's relatively recent, and still a silly way to operate when you could just use normal layout elements ("div" if nothing else) like a sane person and not have to undo the table layout before you can manipulate them properly.