@Gregorius Eddo, I don't know what tool you're using to cut your images but whichever technique it is retains hair details which are blurry and not sharp enough. I'd also suggest rotating sources like this so that they're upright, instead of tilted to one side.

To get the best quality cuts, I would recommend using remove.bg, which is a free online tool which removes the background to an excellent standard, for free and almost instantly.

Here's a couple of videos on how to use it, one when combined with Photoshop and another using photopea.com, which is a free online app so close to Photoshop that it has the same shortcuts, layout and icons.

If you don't have Photoshop, photopea.com is the tool I would recommend to use to tweak the draft cut produced by remove.bg. It's more powerful and versatile than GIMP and other similar tools.