There are many problems with phase detect autofocus that make it inferior to manually focusing using liveview:
Misalignment/calibration errors. AF in not performed using the main image sensor, but a separate AF sensor which is supposed to be mounted the same distance behind the lens. This mounting is subject to a tolerance, as are the position of the focusing group in the lens. This is a problem because PDAF is not fully closed loop, i.e. it doesn't continually refine the focus distance. When it believes it's close enough it sends a command to the lens to move and then terminates. Liveview uses the actual image projected onto the actual sensor so lens tolerances have no effect.
There is a threshold for what the AF system believes as good enough. As mentioned in the previous point, the AF system sends it's final command when it believes the focus distance is close enough. These thresholds were set in the late 1980s when people didn't print larger than 9"x6" from a 35mm film negative. A Canon 5D mkIII RAW will contain significantly more detail than a 35mm neg, the AF system might be happy with getting "close enough" but viewing the image at 100% or printing a large sizes will reveal errors. A good liveview AF implementation can continue until the focus is dead on, or close enough that no improvement is seen on the image sensor by moving the lens.
PDAF performs phase detection by measuring the horizontal offset between brightness patterns detected by two 1-D arrays of pixels. It can easily be confused by repeating patterns which can appear well aligned at different offsets. For subjects with variation principally in one direction (such as stripes) in addition, accuracy suffers, dropping to zero as the angle between the texture and AF sensor approaches zero. Liveview / contrast detect AF and manual focus look at an entire area, not a single line, and is therefore sensitive to detail in any orientation and not as easily confused.
PDAF is performed with the lens wide open. This can cause problems with lenses
which exhibit focus shift when stopped down. Focussing with liveview can be performed with the lens stopped down to the aperture you plan to use, and therefore also offers a realistic depiction of the depth of field you'll get in your image.
Old answer that applied to contrast detect autofocus:
A human can be expected to perform better than the cameras contrast detect AF system in a few scenarios, for example when the subject is moving slightly (such as trees swaying in the breeze) as a person is able to recognise the content of the image and predict its behaviour better than a computer.
A human can, during focusing, re-evaluate decisions about the correct object to focus on (e.g. starting to focus on one area, then seeing another detail start to come into focus which is more interesting). A human can also dynamically vary the size of the region to concentrate on based on content, e.g. focussing on an individual branch, whereas most CDAF algorithms will only consider a fixed rectangular region of interest.
Additionally a human can be expected to provide finer adjustments to the lens position using a mechanically linked focus ring than is possible for the camera using the lens's AF motor.
Outside of those situations, given an appropriately flat, detailed area to focus on, a contrast detect AF algorithm can be expected to perform as well or better than a human, as it is easier for a computer to measure contrast than a person.
