I've seen lots of artists playing with their thumb resting on the top of the neck, but my guitar teacher says it's a must to place the thumb on the back of the neck. Is this really necessary?
Playing with your thumb on the back of the neck generally means you have to bend your wrist more, but gives your fingers greater range since they can extend further from below the neck. If you have long fingers or a thin neck it might not be an issue, but I have above-average sized hands and find that with my thumb on the top I have to lay my fingers flat on the strings (making it impossible to play many notes on higher strings if I'm fretting lower ones). On the other hand, some also play bass notes with their thumb wrapped around over the neck.
In short, there are downsides and upsides to both methods. I think you should do whatever you prefer as long as it doesn't hurt.
If you are a rocker who is just determined to hold your axe in that low-slung "sexy" position, then wrapping your thumb around the neck is about the only way to avoid eventual tendinitis... And that only marginally. If you want the most efficient position and the one least-disposed to cause injury, then adopt the position used by classical guitarists with the thumb below the half-way point of the neck and the wrist essentially straight. Of course, there are intermediate positions as well.... Flatpickers often hold the guitar essentially level, but they are rarely playing wrist-stretching barred chords either. So...Little strain on those important tendons.
It seems to me that this rule is mostly for teaching purposes. Along the lines of "learn this so you can decide for yourself if it's the way you want to hold your hand when you fret". The way I learned was to place my thumb directly behind my second finger, centered on the back of the neck. I learned it, and am comfortable playing like that when that rule applies, but I don't restrict myself to playing like that when the situation calls for another remedy, and comfort also is a determining factor. Probably not a bad idea to learn it and then decide for yourself.
Much of this requires wearing your axe with a strap but probably not folk style(mine is old school where the neck meets the body). Probably un-noticeable with guitar on resting on thigh sitting down.
I think I have something to add here especially on single line playing as chords necessitate certain restrictions to what is possible or probable for most part(however this could be enlarged based on what I want to speak of in this answer). The more pressure you use to grip neck the less energy you have for expression any expression especially if any"speed" of movement is involved. But without leverage no sound of any kind can be sustained for any length of time. So leverage and pressure must find balance as you express something say three adjacent frets 123(first three fingers) over and over(picking first note down or upstroke as well as every other stroke down up or alternate picking but always at least one note not picked).
At the tempo of "Black Friday" by steely dan. Try it with your thumb under the neck and see if the tendency to move the thumb over the neck comes into play and ask yourself why? What's missing from the "thumb under" technique is obviously leverage but with your thumb under the neck your fingers feel like there slipping off the strings and thus goes the battle of finger strength thin neck etc, etc which is way off base IMO.
Thumb under only works if you can find the leverage without the pressure from the thumb in fact I sometimes play without the thumb touch the neck at all meaning the leverage comes from another place(that's what causes physical issues).
The problem is not bad technique instead the issue is why am I choosing to do it they way I do it? if the thumb over the neck is easier why? Here is something about this, the first finger in upward/downward(single string and multi string scale movement) is acting as a CAPO -that is to say as an open string to the rest of the hand. That is why the thumb behind the neck is so efficient. However this can not be seen with out understanding how the other fingers work in concert with this fact.
This is easy to see in triplet play(this occurs in any repeated prase length no matter the number of notes before repetition but usually 3 or 4) : off any finger combination using one string(for simplicity) when the fingers go down they do not hit the string unless there is some circular movement to get them there. They must be targeted according to some pulse(look at David Sudnow's ways of the hand), however this is DIRECTIONAL, that is to say either going down towards string in a pushing action(Push Off) or coming up after touching the string(Pull Off).
Everybody knows the pull off but how many even know what a Push Off even means. This is most easily seen on the high string and the low string, High string means Push off(towards middle of the neck width wise), Low string means Pull off (towards the middle of the neck width wise)meaning the same but in the opposite direction.
The important point here is that this action happens AFTER the note is fretted on the way to the next fret in the phrase THAT is where the leverage comes from not whether or not the thumb is or isn't behind the neck. If the thumb is over the neck you are "short arming" the activity and in certain circumstances that's unavoidable. This is but a brief sketch of what is happening. I found this information I gleamed from watching the activity as it occurred and has made things that were impossible seem easy now. Perhaps another avenue may come to say more.
Note: The terms Push off and Pull off are not about direction as in high to low or low to high in tones because you can push off or pull off in EITHER direction.
High strings can be pulled off and low strings can be pushed off but the drawbacks are obvious except at very high speed where it is harder to notice distinctions in anything happening whereas with all other strings the choices is situational(Pushing or Pulling).
The Middle finger can also be used in this CAPO fashion. The little finger is the only finger exempt?(not known yet). Does not need to be triplet but was first noticed in this activity.
Postscript(New info discovered)
What I have seen is that the constant rotation involving the Shoulder/upper arm/forarm/wrist allows for the different thumb positions.
The starting place is thumb under neck with rotation either counter clockwise(Thumb towards higher strings) or clockwise(towards lower strings) the more frets(neck to bridge) like say for closed position chord voicings, the less rotation away from center(thumb under neck).
Counter clockwise yields thumb over positions and access to less frets(neck to bridge). Clockwise with thumb facing more towards bridge(meaning leverage comes from inside of palm - hence thumb can be lift without loosing leverage).
If hand is rotated clockwise with thumb facing towards neck then pinky side of palm provides the leverage. Even with the thumb in the middle of the neck with no rotation, the Palm itself pressed against the neck is a MAJOR form of leverage for all kinds of single note negotiations. This cannot be stressed enough, this a much better idea then thumb over neck at any descent attempt at soloing at any descent speed(jazz, rock, whatever).
With the newly discovered as a technique unto itself the Pushoff requires minimum stress on the thumb since the hand is CONSTANTLY rotating and the thumb is being massaged underneath the neck. Thumb over especially with Pulloff technique either going up or down the frets is bound to lead to some kind of unmanageable stress on numerous parts of the shoulder/arm/wrist/fingers plus it's much harder to count than Pushoffs.
Your question seems more to be about using your thumb on the middle of the neck versus on the top of the neck, but there's also a third option. When I learned to play cello I noticed that I could easily finger any note on any string I wanted without my thumb touching the neck at all. Using gravity and the weight of my arm was enough tension to stop a string. Thumb position is a similar idea, though including the thumb on the top of the fingerboard.
On a guitar your individual string tension is most likely going to be around the 20 lb. or below level, so you should be able to play without your thumb touching the neck at any point. I wouldn't go so far as to say you should always play like this, but it's a good exercise to remove as much tension from your hand as possible.
In short, your thumb's position shouldn't matter that much, as long as your wrist is straight. It'll change depending on what you're playing; just like how your fingers aren't always going to be spread out to play a major third on one string. Be flexible.
There are certain playing styles which are most effective where the thumb rests or braces itself on the back of the neck. For example in classical and flamenco guitar. But the thumb over the top of the neck isn't necessarily a sloppy technique.
The reason for it in many rock songs is that it's used as a simple way to mute the low E string when playing many variations of E and C shaped chords. Watch an old video of Bill Haley playing Rock Around The Clock, and then play it like that, and you'll understand why.