I wasn't really able to logically understand why blurring an image before sampling prevents aliasing until I really understood the Nyquist theorem. Since the theorem says that in order to not have any aliasing, we must sample at at least twice the image's sample rate (let's call this the minimum target sample rate), by blurring the original image, we effectively remove the high frequency components and lower the minimum target, allowing us to eliminate aliasing with more ease as long as we sample above the minimum target. In other words, instead of increasing the sample rate to hit the bar (which may not be possible when you are downsizing an image), we simply lower the bar. I think this is a good way to not only inductively understand why blurring works for resizing an image, but also have a mathematical basis for how much to blur at the minimum instead of just trial-and-error.
I wasn't really able to logically understand why blurring an image before sampling prevents aliasing until I really understood the Nyquist theorem. Since the theorem says that in order to not have any aliasing, we must sample at at least twice the image's sample rate (let's call this the minimum target sample rate), by blurring the original image, we effectively remove the high frequency components and lower the minimum target, allowing us to eliminate aliasing with more ease as long as we sample above the minimum target. In other words, instead of increasing the sample rate to hit the bar (which may not be possible when you are downsizing an image), we simply lower the bar. I think this is a good way to not only inductively understand why blurring works for resizing an image, but also have a mathematical basis for how much to blur at the minimum instead of just trial-and-error.