In short: Twitch doesn't accept one emote image — it requires 28×28, 56×56, and 112×112 versions of the same art, all with a clean transparent background, before it'll approve the emote at all. RemoveGifBG exports all three sizes from one upload, each with a real alpha channel.
You've got emote art, the background is removed, and you upload it to Twitch's emote manager expecting to be done. Twitch asks for three separate files: 28×28 (chat display), 56×56 (2x/high-DPI), and 112×112 (emote picker and larger displays). Skip one and the submission doesn't go through. If your background removal step only outputs one size, you're now manually resizing twice more — and small emote art is exactly where resizing artifacts (blur, halo, muddy edges) show up worst, because there are so few pixels to work with.
RemoveGifBG's Twitch Emote preset outputs at 112×112 — the largest of the three required sizes — with a clean transparent background, giving you the best starting point to scale down to 56×56 and 28×28 without redoing the background removal at each size. Because the cutout is already clean at the largest size, the downscales stay consistent with each other.
Twitch's actual emote requirements
See also: Twitch emote tool · Full size reference