There are two different so-called “box models”, one adds the padding (and border) to the specified width, while the other does not. With the advent of CSS3, you can luckily switch between the two models. More precisely, the behaviour you are looking for can be achieved by specifying
box-sizing: border-box;
ms-box-sizing: border-box;
webkit-box-sizing: border-box;
moz-box-sizing: border-box;
width: 200px;
in your div’s CSS. Then, in modern browsers, the div will always stay 200 px wide no matter what. For further details and a list of supported browsers, see this guide.
Edit: WRT your edit as to why the traditional box model is as it is, Wikipedia actually offers some insight:
Before HTML 4 and CSS, very few HTML elements supported both border and padding, so the definition of the width and height of an element was not very contentious. However, it varied depending on the element. The HTML width attribute of a table defined the width of the table including its border. On the other hand, the HTML width attribute of an image defined the width of the image itself (inside any border). The only element to support padding in those early days was the table cell. Width for the cell was defined as “the suggested width for a cell content in pixels excluding the cell padding.”
CSS introduced margin, border and padding for many more elements. It adopted a definition width in relation to content, border, margin and padding similar to that for a table cell. This has since become known as the W3C box model.