It's been said that the <TABLE> tag and it's corresponding <TR> & <TD> were meant for charts and data cells, similar to what's used in the famous Excel™ program by Microsoft®.
So why would someone take that spreadsheet and design a website within it?
To novice designers, it seemed like an organized way because the designer didn't take their time to learn the proper way and resorted to <TABLE> tags because they were easier to use. Others found <TABLE> tags as good "cookie-cutter" methods in producing sites faster.
The drawback is that most search engines ignored the content in the <TABLE> tags and simply looked for simple text to pick up as keywords. Other engines simply have a hard time collecting the data especially in nested tables (tables within tables) and occasionally may quit.
<TABLE> tags typically require a lot more bytes on the page than alternatives. The bigger the code in your HTML file, the longer it takes to render. Imagine that on low bandwidth connections!
<TABLE> tags are fine for images and videos that have no text, charts and small data that belong in them. Other than the beforementioned content types, tell your designer to clean up their act and get your site done without using table tags.