I'm currently teaching one of my granddaughters to play the piano. At this stage you spend a lot of time getting the pupil to play in time, that is, making sure they understand the relationship of each note to another in an almost a mathematical sense. One crochet has to be as long as another crochet, a semibreve has to be held the length of four crochets and so forth. It's all very relative. With a fast piece the crochet is shorter than it is in the slow piece, and as a longstanding player of music, you take this for granted, often failing to realise that it's not as obvious to a pupil as it is to you.
And as time goes on, and children play more complicated music, you begin to teach them that the first crochet isn't necessarily quite as long as the second crochet, or vice versa, because you give more emphasis to one than the other. And that one bar may be stretched out longer than the previous one, even though they're both strictly speaking the same length. I've just been practicising a piece for the Brass Band competitions with a cornet player, and of course there are different 'speeds' for different sections (meaning that the crochets, for instance, aren't the same length in the fast section as they are in the slow) but even within the sections, notes are stretched, sped up and generally twisted according to the mood of the piece at that point. Music is actually hugely fluid, and this is a difficult thing to teach.
I saw a film years ago, a documentary about Isaac Stern going to China after the Cultural Revolution, called From Mao to Mozart. There were plenty of young Chinese musicians after the Revolution, and they were playing Western music, but they had no sense of the feeling, the rubato, the shifting of pace that is common to this kind of music. Western influences in China during the Cultural Revolution were banned,
and the musicians lost touch with the way the music was played. They played strictly in time, and of course, it sounded like clockwork. There's a time and place for this in music, but it's rare by comparison with the normality of pulling music about like plasticine. You get to a stage in life where you never think about this, you just do it.
As a footnote to that movie, I remember a pitiful scene in which a music teacher told us how he'd been locked in the equivalent of a cupboard for some long time during the Revolution; the Red Guard did horrific things to artists. In spite of that, after the Revolution's worst excesses were over, he continued to teach.