STOP USING Focus and Recompose. When you focus using centre AF point and then recompose your shot, you tend to shift the focus plane behind the persons head and eyes are out of focus, So intead compose and then select an AF point thats closest to the eyes.
this is more and more important the faster the lens is. 1.2, 1.4, 2.8 with a shallow depth of field. if you are stopped down and have alot of focus depth then continue to use Focus and Recompose.
See this illustration.
See how recomposing shifts the focus plane!
.... image deleted to save bandwidth ....
Here is why I totally disagree with your statement to "STOP using Focus & Recompose".
First, I'm going to assume that the average distance that photos are taken of people is about 6 feet (72 inches). The distance may vary but say 6 feet is an average distance.
Second, assume that the focus point is the closest eye of a person.
Third, the distance of recompose is 26 inches as shown in the figures below. My experimentation has shown that 26 inches recompose is pretty much on the high end of recomposing at a subject to sensor distance of 6 feet.
Forth, the camera used is a Canon 7D DSLR.
(Note that the drawing below was done via computer so the measurements are accurate.)
FIGURE-A:
Figure-A shows the sensor to focus point distance of 6 feet (72 inches). The shooter half presses the shutter and locks focus. Then the camera is pivoted on the axis of the sensor to position the the subject on the left side of the frame. The recompose amount is 26 inches as shown. ---- In this ideal recompose where the axis of rotation is at the sensor, the distance from the subject's eye to the sensor remains at 72 inches so focus on the eye remains perfect.
FIGURE-B:
Figure-B shows a worse case recompose where the shooter held the camera steady and pivoted at his neck, which moves the sensor toward the right. The distance from the focus point (subject's eye) to the sensor is now 72-1/4". This is a change of 1/4" in distance.
Here are the depth of field calculations for two scenarios.

DOF calculator at:
http://www.dofmaster.com/dofjs.html
The first is a worse case of using a focal length of 70mm and a large aperture of F/2.4 shooting at a distance of 6 feet (72 inches). (One would not normally be using a focal length of 70mm at a distance of 6 feet but I used 70mm as worse case.) Note that the depth of field is 2.34 inches. Note that the eye to sensor distance increase of 1/4 inch (0.25) in this unrealistic worse case is well within the DOF of 2.34 inches. The eye is still in sharp focus.
The second scenario is a more normal case of using a focal length of 24mm and the same aperture of F/2.4 at a subject to sensor distance of 6 feet. Note that the DOF is now a whopping 19.1 inches. A HUGE amount more than the 1/4" increase in eye to sensor distance.
At either a focal length of 70mm or 24mm, the eye remains in sharp focus for all practical purposes. Also note that the large aperture of F/2.4 that I used is a "typical" worse case since using smaller apertures would INCREASE the depth of field even more.
THE REAL WAY TO FOCUS & RECOMPOSE:
Rather than holding the camera in the same position and pivoting the body or at the neck to recompose, the better technique is to recompose the camera by using the wrists. Like this youtube video shows at 4:37 in the video:
Focus & recompose technique by Vail Fucci
A practical method would be to recompose using mostly the wrists but with some pivoting at the neck. This would probably result in about half of the distance change that is shown in Figure-B above. So the eye to sensor distance change might be 1/8 inch which is even less than the 1/4" shown in Figure-B.
SUMMARY:
So frankly, I think you are doing beginner shooters a big disservice by telling them in your title and first post to "STOP using focus & recompose" or their subjects will not be in focus.
If shooting at very close subject to sensor distances, like close ups of flowers or insects, then yes, focus & recompose can lose subject focus. In those scenarios, it's best to keep the camera still and select the focus point. But those are specific situations. Not the approximate 6 feet distance shown in the image you posted.
Similar to some other shooters who have posted in this thread, I've also been using focus and recompose for my normal shooting for umpteen years and my subjects have been in sharp focus.
So my suggestion to beginner shooters is "DO USE focus & recompose" for normal shooting distances! It's a LOT, LOT faster to focus & recompose, than to manually select focus points by using navigation buttons or even touch screen.
My $.02 anyway,
Sky