Hair and fur have narrow strands and partially transparent edges. A single aggressive background-removal setting can erase those strands or replace them with an unnatural hard line.
Diagnose before changing controls
Place the cutout over both a pale and a dark background. If you see background color trapped around the hair, it is a color fringe. If strands vanish, the mask is too tight. If background patches remain, the mask is too loose. Those are different problems, so one slider cannot fix all three.
Refine in small passes
In the NexTools BG Remover, try modest edge softness and shrink or grow adjustments. Use the color-fringe control when the old background bleeds into the subject. Switch to erase or restore and touch up only the affected areas. Compare against the original after each change; too much cleanup can make hair look painted.
Check at normal viewing size and at 100%. A microscopic edge imperfection may not matter in a full-frame image, while a large halo certainly will. Save a transparent PNG and preview it on the kinds of backgrounds a buyer might use. That final context check is more informative than judging the cutout on a checkerboard alone.