Things aren't always what they seem. On edges, the color of the pixels is a blend of the two colors on the two sides. Fuzzy select and color select select them totally or totally ignore them depending on threshold. So select+delete will either leave a faint rim (low threshold) or create a jagged edge (high threshold) or both (and there is no good threshold...).
In addition, the ants show where the 50% mark of the selection is, so if the selection is fuzzy, it sits in the middle of the fuzz area, and there are partially selected pixels outside of the ants line. If you delete the selected pixels these partially selected pixels become partially transparent.
In fact with the sharp edges in your pictures you are facing about the same problems as people removing background around logos. See here form some hints.
In addition, the ants show where the 50% mark of the selection is, so if the selection is fuzzy, it sits in the middle of the fuzz area, and there are partially selected pixels outside of the ants line. If you delete the selected pixels these partially selected pixels become partially transparent.
In fact with the sharp edges in your pictures you are facing about the same problems as people removing background around logos. See here form some hints.