From the (surprisingly poorly designed) W3C website:
A certain trend among designers, believing that small text gives a Web page a sleek appearance and provides more space per “page” for actual content, sometimes results in the use of unreasonably small font sizes.
Unfortunately, this does not go well with the diversity of platforms used to access web pages, from portable devices with tiny screens to projection devices hooked to computers. And even within a specific platform, text settings may vary.
The problem here is a basic usability and accessibility issue: a good design should look good without requiring the user to enlarge or reduce the text size.
Another trend goes in the other direction and make the copy too big. Different people have different preference and needs; some like small type, some need bigger letters. If you keep the size of your p as 1em, which is the default, each user will have their preferences respected.
A common mistake is make type too small to look cool. Just leave the font-size for p alone.