Watch the Left-Hand Thumb Position online guitar lesson by Bruce Arnold from Guitar Physiology Survival Guide
In its position on the other side of the neck, the thumb needs to stay between your index and middle finger. Too often students lag their thumb behind as they move up the neck. This causes instability and changes the relationship of your fingers to thumb thus changing the signals coming to and from your brain. Remember we want to keep everything the same so your brain only has to learn one technique not a different one for each note you play.
The thumb is NOT putting pressure against the neck but it IS touching the neck. You will push in certain instances, as when playing a barre chord but if you are just playing single notes or even a couple of notes, the amount of physical energy you really need is so small that you do not need to form a vice grip between your thumb and your finger.