My mantra, which has become a pet phrase, worn thin in the minds of some, something by which to create a cartoon image of me, I suppose. The first phrase.
Singing is mental. The problem is language. Some have supposed that when I say that, it is meaning that one can sing well simply by thinking about it. Not exactly the truth. There is also a corrollary; listening is mental. For there is also the perspective of the listener, who is also sometimes the singer. How does the audience perceive your singing? How do you perceive your singing? Or, the singing of others? For that makes a difference. A singer can be on pitch and have usable volume, the two aspects I care about if discussing a purely technical issue. And yet, still not inspire or the tone is perceived as wrong by others, sometimes including the singer.
A teacher asks you to make a sound or vocalize in a certain way and you "don't like" the sound because of what it sounds like to you and the emotional content you give that sound. For example, a teacher leads you through a falsetto exercise and you already have the attitude that falsetto is weak and of no use to any singer. So, you are already deciding what is of use from the teacher and that decision is mental. And because you have that mental thing to reject falsetto, you will not receive whatever value there is to be had from that.
The same thing with some exercises in twang or even nasal resonance. You may decide that sound is "too nasal." Compared to what? It may not matter, as you have already "decided" that the sound is not for you, even in training. And the benefits you could gain from well-tuned nasalance will be lost before you start.
Adjusting your perspective or accepting that your mentality will affect your singing is the first step toward improving singing. Thinking about singing doesn't make you a better singer. But having the open perspective will allow you to work exercises given by your teacher, even if you do not see the value at, first, and that will lead to better singing. But the first step is "I will cast aside my aspersions to odd sounds, my prejudices of what is good or not good singing and instead, follow the teacher's path and see where it takes me."
And each person can need something different. Some people do great with lip bubbles. For me, it was too much tenson in the mouth since I have these thin, german lips. But a classical coach gave me warm-ups with the v sound, which is more appropos for me. Because then, the tendency is to lose too much air, which requires you to more correctly control the air, not having the back pressure of closing lips to help. Kind of a sink or swim thing, which worked better for me. It requires a more proper level of initial vocal sound and a need to start out in breath management, rather than engage it later. I also can speak some spanish, and unlike most americans, I can do the spanish b sound, which is similar and even more appropriate for a v sound, as it is a more subtle articulation, in my amateur opinion.
Another reason singing is mental is because singing is playing a musical instrument but not like any other musical instrument in a few important aspects. I also play guitar. Six strings on a construction of wood. I play different notes by pressing different strings at different frets and striking the strings with a plectrum or the fingers of my other hand. (True story, I am left-handed and play the guitar right-handed.) I can physically tune the guitar to specifications and can accurately reproduce exact notes through simple mechanical motion and I can "see" what I am doing.
Not so with singing. The instrument is inside my body. I do not reach into my throat and use my fingers to change length and thickness of the vocal folds. I do not stick a finger in my mouth and move the soft palate hither, thither, and yon. I do not have a spatula to spoon a note to a particular spot of resonance. It is all done with imagery and sensation, as interpreted by my brain.
I don't physically grab the muscles in my body to play the air like the bellows of an accordion or bagpipes. That comes from a thought.
So, I say that singing is mental because it is, no matter how trite that sounds.