It has been a bit since I've researched why tables shouldn't be used for layout so I'm not full bottle. Perhaps I'll have to write an article.

Linear layout issues come to mind first: https://www.w3.org/WAI/WCAG22/Techniques/failures/F49

Then there are issues with screen readers and how they interact with tables. Tables convey that they are tables, so screen readers treat them as such. Sometimes this means reading headings in between cells to help orient the user, and sometimes it means they'll add numbers for orientation. A bit of detail here: https://dequeuniversity.com/rules/axe/4.1/layout-table

If there are any mistakes in the markup, then it can completely throw off the layout in the accessibility tree without having any visual indication that something is wrong. Perhaps most importantly, tables are very rigid and inflexible, so if trying to do anything more dynamic or out of the boxy flow it usually means messy hacks.

If you're really careful you can sometimes get away with it, provided your site is extremely rigid in layout, but it generally ends in an inaccessible mess that is inaccessible in ways that people don't even bother to document nowadays. Just use flex and/or grid if you're targeting modern browsers. Much easier to author and much better for users.