Why do lots of games have Direct X 9 and 11 options, but NOT DX10?

This is because Windows XP only supports DirectX 9. DirectX10 was added with Vista, but Vista also got a backport of DirectX11 from Win7 (Platform Update), so Vista/Win7/8 can use DirectX 11 and Windows XP DirectX9. And because providing Dx10 rendering path makes no sense when you can use the better DiretX11, most games only offer those 2 modes.