Relaxing shoulders
The idea behind any martial art is to be efficient. You will not be efficient if you are using muscles that are unnecessary for a particular action.
Try raising your arm slowly and pay attention to which muscles are really doing the action. Depending upon the direction in which you raise your arm, you will be involving mostly the deltoid muscles of the shoulder area. (Anterior deltoid-if raising to the front, middle deltoid-if raising to your side, posterior deltoid if raising to the rear)
The trapezius, on top of the shoulder and upper back, is the muscle used in shrugging your shoulders-an unnecessary motion in most raising arm movements. The function of the traps in lifting your arm would be in stabilizing the entire shoulder, as such it would only contract somewhat. That is what is usually meant by ārelaxā the shoulder while raising your arm.
A misunderstanding is that relaxing the shoulder would mean that there is absolutely no tension in the area. If that were so, there would be no movement since movement is caused by the contraction and relaxation (that is you need both) of muscles.
What most people try to do in Tai Chi is to feel movement originate in the body, rather than in the limb and then feel that energy travel through the body as a wave. This is accomplished with a minimum of muscluar contraction.
If you keep your elbow lower than your hand when you raise your arm, that will help to limit tension in the shoulder to the appropriate amount.
I agree, you can use the lats to keep the shoulders down, but this will create new tension in other muscles, so you should keep the lats loose in rasing your arm as soon as you can feel which muscles do what.
If you are extending your arm, be sure not to ālock outā your elbow-that is, do not go to 100% extension as that will create extra tension and if it becomes a habit may lead to problems with your elbow or shoulder joints.
In extending the arm totally different muscles come into play, such as the serratus in your back and sides, but these are not usually considered āshoulderā muscles.