From the page lined above
To align data in a tabular structure we can use a common table using the HTML tags <table>, <tr>, <td> nonetheless we all know that by using that we are violating the latest web standards, right?
Conditionally right, and also conditionally wrong. "Using tables is wrong" is not a tautology. So claiming that it is wrong, without stating when it is right or wrong, is not at all good. I'm guessing a lot of people have not understood when and why it is wrong to use tables, and therefor simply learnt that it is wrong. And then they teach others that it is wrong, when really, it is only sometimes wrong.
HTML markup is supposed to be semantic - the elements indicate what type of content is found inside it. Using tables for design reasons is just as wrong as making a text in the middle of a paragraph big and bold by using any of the header elements <h*>.
<h4>This really is a header. Ok to use header element</h4>
<p>You should <em>always</em> validate your code, and since the header (block)
elements aren't allowed in paragraphs, you should allready be aware that you've
done something bad. Apart from manually styling the text, it's of course possible to
use the <em>non-semantic</em> elements <b> and <i>. But since HTML is
supposed to be <em>semantic</em> those elements were removed. You do instead
have the em(phasis) and strong elements, which do carry semantic meaning, while
they do not at all tell the browser how to present these elements' contents.</p>
<p><strong>Never use a table for design purposes, just like you would never use a
header element for something which isn't a header. Never use deprectated elements
that have no semantic meaning, such as font, i and b. On the other hand, always use
header elements for headers and tables for tabular data.</strong></p>
<p style="font-size: 22px; font-weight: bold;">No no no. Use a header element instead</p>
<p>This is <b>also</b> <h4 style="display: inline;">really</h4> bad</p>.
If people are against using tables even for tabular data, then they are wrong and have not understood the purpose of the different HTML elements. After all, you could use only one element (apart from for posting form data), and use CSS to make that one element be a block, a table, inline, bold or whatever else you desire.