I think it's worth pointing out that there isn't really a huge bloc of people who argue Sikhi doesn't believe in reincarnation, it's more like a distribution of individuals and that too recently.
The main arguments I've seen are (and note that I'm not necessarily saying I agree/disagree with them, I do agree w/some of them and disagree with some):
-Sikhi is concerned about the here and now, afterlife is irrelevant
-Reincarnation is a cruel system (Jugraj himself gave the example of a disabled child being born that way because he did bad actions in his previous life)
-The GGS mentions heaven/hell as well (both in the Dharmic sense of Narak/Dharamraj which can be seen as metaphysically compatible with reincarnation and in the Abrahamic sense of jannat/shaitaan which is a bit more complex)
-There are other things in GGS which would be odd if taken literally (dasam duar, 5 elements, so on) and since this thing is odd (and somewhat goes against our current scientific understanding of the body and mind) ergo it is not to be taken literally.
-Reincarnation is a "hindu" belief
Again, I think a large thread on this topic would be very fruitful for many members, especially when Jugraj spent a long time on discussing it in his video.