Your diagram is essentially correct. The key point is that depth of focus is not “symmetrical” in the sense that the image distances on either side of best focus must be equal.

What is symmetrical is the acceptable blur size: points displaced on either side of the best-focus image plane can produce blur circles of equal radius. That does not require the distances in image space to be equal.

Using thin-lens geometry, the near and far image locations generally will not be spaced equally around the plane of best focus. Likewise, in object space, near depth of field is usually smaller than far depth of field. As magnification increases and the subject approaches the focal distance, the near and far portions become more nearly equal, but not generally identical.

Also, be careful with the term “depth of focus.” It is often used for image-plane tolerance (sensor/film placement, tilt, film curl, front/back focus tolerance), which is different from depth of field in object space.

So: your unequal distances are not necessarily a mistake; the confusion is in assuming depth of focus means equal distance on both sides of focus.