Essentially, one of the major changes from Windows NT/2000/XP to Vista has been a complete re-engineering of the OS core (the kernel). While the basic design of XP is very old, it has been patched and upgraded to keep it up to date. However, the changes in Vista are more substantial than just simple updates.
DirectX is an 'API' - it's a language, a vocabulary, of commands that programs can use. A DirectX compatible card is able to understand those commands - or the card has a driver which can understand them, and translate them into a form that the electronics can understand.
Part of the changes in Vista are a complete overhaul in how card drivers communicate with programs and with Windows. These changes were done to improve stability and speed. This means vista drivers need to be designed in a different way to XP drivers. DirectX 10 takes advantage of some of these changes in order to improve performance.
While, technically, making DirectX10 work on XP would be possible - it would be difficult. It would require redesigning the DirectX 10 system, so that it doesn't rely on the new stability/performance features of Vista, redesigning the card drivers so that they are XP compatible, etc.
It would be so much work that it would be almost as much work as designing and building DX10 in the first place. Now put yourself in MS's position - would you spend 10s or 100s of thousands of man-hours, at a cost of millions of $ - to upgrade a product that is nearly 6 years old, and a product for which you already have a superior replacement?