Animations in a GUI are in principle absolutely fine. The problem is when the animation gets in the way of the task the user is trying to do. For example, on windows, when you click a window in the taskbar which is currently minimized, instead of instantaneously appearing maximized it will do an animation which transforms the small start bar icon into the full window. This only takes 0.1 seconds but this adds up. If we assume there are 100 million users of Windows every day and each of those users maximizes 20 windows in their use, there are 100,000,000 * 20 * 0.1 seconds = 6.33775293 years wasted every day due to this stupid algorithm. This single animation is costing the economy a large amount of money. It seems ridiculous that it could waste so much time but it does – the time lost in watching that animation is not retrievable.
The key to using animations in GUIs is to make them not slow down what the user is doing. For example, instead of showing a slow transform of the window becoming larger and larger, it should instantaneously appear at full size and then have some kind of animation like a glowing effect around the window or a shockwave emanating from it.