Why are downscaled sprites blurry?

It depends on the filtering type you have enabled. If your sprites are scaling a lot, make sure they have mipmaps and not point/nearest filtered.

In this case, part of what you are seeing is that you have very thin lines. As those lines become smaller than one pixel, the GPU has to try to filter, but it can only do so much and you get patterns like the one above. Generally you want to author your art at the display resolution and avoid very thin features on images that will scale a lot. Alternatively, you can use geometry for these shapes or you can custom author mip-maps.