Taking the second part of his comment first, yes, you can crop out a face portrait from a wide-angle picture if you start from a photograph with a large pixel size. In practice, though, relying on wide-angle tends to lead to certain short-cuts which I will describe below, and which do not give good results.

 
The pitfalls of wide-angle lighting

The first part of this reader's comment, however, concerned lighting, so let me answer that before we talk about zooming. Contrary to his point, I think it is especially if you use wide-angle that you can face problems with lighting. The reason: The camera's software tends to adjust itself for the average lighting in the entire scene. If there are bright objects in the scene, it adjusts itself for them and your face may end up as a relatively dark object by comparison.

Take the pictures below for example. The objects were set up in a room by a window just as described in the earlier essay. Picture 1 was taken with a wide angle; so unavoidably a section of the window was included in the frame. Since the outside was much brighter than the inside, the "auto" setting for exposure would try to get an average between the bright outside and dimmer inside. The result would be that the indoor objects (or subject, i.e. you) would be too dark.

Even if you cropped the face out from Picture 1 into Picture 2, it would still be unsatisfactory. The bust is far from white and the teddy bear's fur dirty and dull.

Pic 1: at 2.5 metres, wide-angle, "auto" setting for exposure		Pic 2: cropped from Pic 1
Picture 3 on the right shows the result when the camera is zoomed in so that the objects of interest fill much more of the frame and extraneous elements, especially the bright outside, are excluded. The result is much better.		Pic 3: at 2.5 metres, with zoom x 3, "auto" setting for exposure

It is for this reason that I advise zooming into the face that you're interested in before you take the picture, rather than take a wide-angle picture and hope that the face comes out right amid many other objects in the scene. 

Hence, if you're doing a DIY self-portrait in your own room, it means setting up a surrogate object to represent you, so that the camera can be zoomed and focussed correctly beforehand.

 
The effect of zooming

Pic 4: At 3 metres, no zoom, i.e. wide angle. Pic 5: At 3 metres, zoom x 2 Pic 6: At 3 metres, zoom x 3 Pic 7: At 3 metres, zoom x 5 or x 6 Pic 8: At 3 metres, zoom x 8

Before I move on to explaining the bad short-cuts, I need to touch on telephoto zooming. In my earlier essay, I had advised that do-it-yourself self-portraits should be taken with at least 2-times zoom, better yet, 3-times zoom. Unfortunately, I omitted to explain why in that article itself, but I will below.  For this degree of zoom, to capture a half-body picture, you will need a distance of 3 metres from camera to subject, which can inconvenience you if you're doing it indoors and your room is small or cluttered. The pictures of Sam on the left will approximate the zoom results when taken at 3 metres. I say "approximate" because no two cameras are the same.   Aesthetically, the best results are Pics 6 to 8, taken at 3x, 5x and 8x zoom.

 
Short-cuts, not recommended

The question is, why not start from the picture taken with wide-angle (Pic 4), and crop out similar portraits from it? As I have mentioned, theoretically, yes, you can. You'd get these:

Pics 4, 9 and 10

The first crop (Pic 9) gives a result similar to the 3x zoom picture (Pic 6 above). The second, tighter crop (Pic 10) mimics the 5x zoom picture (Pic 7 above). Generally the results are fairly acceptable, provided the face is correctly exposed and the sharpness is there. However, to my eye, I can see 2 things wrong about them already -- see box on right.

However -- and this is where trouble begins -- you are likely to think: "Hey, why do I need to put my camera 3 metres away? The face is too small in the original picture."

By this reasoning, or because your room is cluttered and you just can't find 3 metres of clear space near a window, you are tempted to work with a shorter distance, say 1.5 metres.

At 1.5 metres, no zoom, i.e. wide angle.

Pic 11

Or even less, say, 0.6 metres from your face, hand-held because you don't have a tripod perhaps. All the time using wide-angle.

At 0.6 metres, no zoom, i.e. wide angle.

Pic 12

Would the results be satisfactory? Clearly not. There is very obvious distortion in the last example. The upper half of the face is exaggerated; the chin reduced. There is a puffiness of the cheeks.

You might not have noticed it immediately but the distortion is noticeable even in Pic 11, taken at wide-angle from 1.5 metres, as you can see by comparing the cropped version with a zoomed version.

Cropped from Pic 11: At 1.5 metres, no zoom (wide angle)		Pic 8 for comparison: At 3 metres, zoom x 8, not cropped.