I think, I will read something about sacrifice in Ancient Egypt and then will come back for more. I'm pretty sure Encyclopaedia Of Religion And Ethics should hold a comprehensive paragraph, though it all depends on who wrote it.
Unfortunately, sacrifice in Ancient Egypt was such a footnote, it was jammed into the article of
Sacrifice (Semitic) in the Encyclopaedia Of Religion And Ethics. Unfortunately again, Egypt was rather independent of other semitic cultures, and therefore the article barely holds anything in value related to Ancient Egypt. In fact, I only found two notes related directly to Egypt:
Encyclopaedia Of Religion And Ethics said:
In Egypt part of the daily temple services consisted in clothing and decorating a figure of the deity, and then setting before it an offering of food — bread, geese, beef, wine, and water. These, after standing a while before the god, were most probably appropriated by the priests.
Encyclopaedia Of Religion And Ethics said:
In Egypt, the king began his reign with a sacrifice to Min, the god of fertility, in the presence of the statues of his ancestors. 'A priest presents him with the royal sickle, with which he cuts a sheaf of corn ; he then strews it before the white bull, symbolizing the offering of the first-fruits of his reign. He then offers incense before the statue of the god, while the priest recites from the mysterious books of the "dances of Min."
The last quote is... well, dubious. It might've been a valid ritual at some point of ancient egyptian history, but it definitely did not hold throughout the whole time of Ancient Egypt. In fact, the previous note should be applied to pretty much everything when Ancient Egypt is discussed: people tend to forget that Ancient Egypt existed for more than 3000 years, and that is more than our current christian civilisation lasts, and over the course of several millenias culture and people change a lot.
Anyway, I do not think this anyhow provides any light onto the issue. I still feel it would be correct to provide a link to the book:
Vols. 6-12 edited by James Hastings, with the assistance of John A. Selbie and Louis H. Gray.
archive.org
Sacrifice is the very first article in it, so you should not have any troubles finding it. Though reading through the Semetic article, I think the author only bothers to describe customs and traditions of cultures in great detail, but really doesn't bother to ask why it was done in the first place. You still might want to skim through it - article about every culture has its own author, and other authors might be more inquisitive, plus the whole thing is not that long and offers a glance at number of cultures, including Celtic, Greek and others.
A more interesting discussion has been found in another volume of Encyclopaedia, under the title
Human Sacrifice (Semitic). However, it mostly discusses all the evidence for and against human sacrifice in Ancient Egypt. It mostly boils down to "Ancient Egyptians were semitic, so they must've had human sacrifice at least at some point of their history, even if they developed it independently", which is a dubious notion, yet the author of this particular article seem to feel it is true. Despite that, he rather fairly introduces everything about the topic, both for and against it. And it once again confirms that we do not have any concrete evidence about existence of human sacrifice from ancient egyptian documents - all the notions in favor of human sacrifice come from late period roman and greek tourists, which is obviously unreliable. The author says that "in general, the native is not so likely to record facts and practices which for him are commonplaces as is the foreigner to they are less familiar", but it is a wishful thinking at best: we have a lot of ancient egyptian documents from all eras, a lot of which mention sacrifices of all kinds, and some of which describe the animal sacrifice in great detail, but there's not even a word about human sacrifice in any of said documents.
In general, it is nowadays accepted that even if human sacrifice was ever a thing in Egypt, by the times known to us all actual human sacrifices were already substituted with something symbolic, like the aforementioned ushebti.
The continuation of the article about other semitic cultures where the evidence is undeniable might be of interest to you though, because the author writes in the premise: "The discussion of this subject falls naturally into two parts: a marshalling of the evidence for the existence of the rite, and an attempt to deduce the purposes and ideas underlying it". Unfortunately, I do not have the time to read it, so I will leave you a link:
Vols. 6-12: edited by James Hastings, with the assistance of John A. Selbie and Louis H. Gray.
archive.org
Page 862 for Human Sacrifice (Semitic), page 840 for Human Sacrifice in general.
Finally, I found that bit about sacrifice of the bull which I've mentioned earlier, though turns out it wasn't quite about sacrifice either - the bull was sacred, not sacrificial; my memory just got a bit mixed up. The whole article is on russian, so I think providing a document will be useless, but I'll translate the bit I find interesting:
"Killing the sacred animal was a crime against its whole kind and against the king of said kind - Apis, Mnevis, et cetera. It was equal to killing a God and called for tragedies upon the whole country ... To placate a God, sacrifices have been made to a sacred animal that was about to be killed. A pompous funeral was arranged. If an animal was eaten, its bones were to be buried. Otherwise, it was embalmed, wrapped in bandages and gilded cartonage; amulets were given to it and its tomb has been made as if a human was buried in it. Either a special tomb was built for it, or a human tomb without a mummy in it was used. There were also collective tombs for sacred animals".
Pardon for the hasty translation - I'm kind of in a hurry, but I hope it is understandable. In two words: the reasons are purely religious in this case.
Hope I was able to help at least somehow, though I feel that in general I didn't anyhow answer the question at hand. Sorry.