Earlier quoted context omitted.
Computer UIs need animations for the same reason they need shadows, gradients, and momentum: because these are aspects of the physical world that we already know how to interpert, so can be used "for free" to aid our understanding of the UI. Not using animations would likely be more taxing on our visual processing because nothing in the world moves discontinuously, so that would be a new thing to learn when using a c…
This appealing fallacy is part of the reason, but way too broad in general (and is also not reflected in the flat design land of today, but even before that almost nothing was really skeumorphically close to reality), so let's try to apply it to this specific case: you usually click on a slider, not drag it. So in this case, there is nothing "physical" on the user's intuition side that corresponds to the slider slidi…
Because the “knob” changes position. Like in the real world, objects can’t disappear in one place, and then instantly appear in another. Animating a UI state change in terms of a move transition can help people to understand how both end-states are logically connected to each other. The animation resembles the mechanics of the slider knob being a “perpetual entity” that can move between two positions, rather than the slider control as a whole being some sort of static icon that is instantly swapped out for another static icon once I click on it.
Whether or not animations are necessary might still be arguable. I suppose it depends on the complexity of the UI control, on personal preference, and certainly also on the general level of technical familiarity of the end-user.