What reasons does the Bible give for why the tribe of Levi was chosen to have the priesthood and temple duties?

From Wikipedia:

The books of Exodus, Leviticus and Numbers maintain that Aaron received from God a monopoly over the priesthood for himself and his male descendants (Exodus 28:1).

The family of Aaron had the exclusive right and responsibility to make offerings on the altar to the God of Israel. The rest of his tribe, the Levites, were given subordinate responsibilities within the sanctuary (Numbers 3). Moses anointed and consecrated Aaron and his sons to the priesthood, and arrayed them in the robes of office (Leviticus 8; cf. Exodus 28-29). He also related to them God's detailed instructions for performing their duties while the rest of the Israelites listened (Leviticus 1-7, 11-27).

Aaron and his successors as high priest were given control over the Urim and Thummim by which the will of God could be determined (Exodus 28:30). God commissioned the Aaronide priests to distinguish the holy from the common and the clean from the unclean, and to teach the divine laws (the Torah) to the Israelites (Leviticus 10:10-11).

The priests were also commissioned to bless the people (Numbers 6:22-27). When Aaron completed the altar offerings for the first time and, with Moses, "blessed the people: and the glory of the LORD appeared unto all the people: And there came a fire out from before the LORD, and consumed upon the altar the burnt offering and the fat [which] when all the people saw, they shouted, and fell on their faces" (Leviticus 9:23-24). In this way, the institution of the Aaronide priesthood was established.

When God killed all of the firstborn in Egypt he passed over the houses of those Hebrews who had put blood on their door mantels:

Exodus 12:29 And it came to pass, that at midnight the LORD smote all the firstborn in the land of Egypt, from the firstborn of Pharaoh that sat on his throne unto the firstborn of the captive that was in the dungeon; and all the firstborn of cattle.

And in return for passing over those children of Israel, he declared that all the firstborn of Israel both human and livestock be dedicated to him. I will not go into what that dedication meant since it has no bearing on your question.

Exodus 13:2 Sanctify unto me all the firstborn, whatsoever openeth the womb among the children of Israel, both of man and of beast: it is mine.

When the Tabernacle was built and erected God then took the tribe of Levi in place of all the firstborn of Israel as laborers to move the Tabernacle from place to place and care for it’s many parts.

Numbers 3:45 and 46 Take the Levites instead of all the firstborn among the children of Israel, and the cattle of the Levites instead of their cattle; and the Levites shall be mine: I am the LORD. 46 And for those that are to be redeemed of the two hundred and threescore and thirteen of the firstborn of the children of Israel, which are more than the Levites;

So the entire tribe of Levi became thr redemption for all the firstborn children of the other eleven tribes.

Gen 49:5-7 was indeed a prophecy concerning Simeon and Levi.
They were scattered/dispersed due to their anger and when you go into Exodus we see someone who represented this prophecy as Moses who was from Levi tribe. Moses was first taken away from Israel during his birth after Pharaoh ordered the killing of male child that was born. He then went to live in Egypt after being adopted by Pharaoh’s daughter.

The prophecy written in Gen 49:5-7 is then fulfilled when Moses killed the Egyptian who was beating a hebrew slave. Moses later ran away from Pharaoh and fled to Midian after Pharaoh heard the news of the Egyptian that he killed. This is written in Exodus 2:11-23. Here we see that Levi tribe was chosen and the representative was Moses who became the promised pastor at that time and led Israelites out of Egypt (Hell) to Canaan (Heaven).

We may find one explanation that is based on lineage. This is outlined first. The second explanation is based on a tithe (tenth). The second explanation may be found in the Book of Jubilees. This is shown second.

Moses and Aaron

The original reason for having a separate priestly tribe is because the children of Israel were afraid of God and His voice. They wanted someone to stand in their place. This fact appears to be the only reason why the Levitical tribe was chosen to represent the other children of Israel.

And all the people saw the thunderings, and the lightnings, and the noise of the trumpet, and the mountain smoking: and when the people saw it, they removed, and stood afar off.And they said unto Moses, Speak thou with us, and we will hear: but let not God speak with us, lest we die. Exo 20:18-19

So, they chose Moses the son of Amram the son of Kohath the son of Levi (see Exo 2:1-2, 6:18, Numbers 4:4-14).

Moses had led them out of Egypt with the help of his brother Aaron. These two were Levites (see Exo 4:14).

The assumption was that because Moses could behold God and live that his brother Aaron and his sons would be able to do so also.

Subsequently, while Moses is on the Mount receiving the 10 commandments, Aaron and the others are in the valley below collecting gold and building a golden calf.

Moses descends, sees their idolatry, and cries out, whoever is for the LORD, rally to me. The sons of Levi is the only tribe to come to his side.

This is one reason the Levites were chosen to be the only priests under the Mosaic Covenant.

And when the people saw that Moses delayed to come down out of the mount, the people gathered themselves together unto Aaron, and said unto him, Up, make us gods, which shall go before us; for as for this Moses, the man that brought us up out of the land of Egypt, we wot not what is become of him. Exo 32:1

Then Moses stood in the gate of the camp, and said, Who is on the LORD'S side? let him come unto me. And all the sons of Levi gathered themselves together unto him. v 26

In short, Moses was a Levite who was able to "withstand" God. Aaron was his brother. Moses anoints Aaron into the priesthood.

Book of Jubilees

This was an influential book that has an oral tradition. Some groups believe it to be scripture. It gives three ideas, but I focus only on the third one as the most intriguing and sensible explanation.

Jacob had 12 sons. Reuben, Simeon, Levi, Judah, Isaachar, Zebulon, Joseph, Benjamin, Dan, Naphtali, Gad, Asher.

Jacob had promised to tithe everything to God after his dream. This would include his sons.

And this stone, which I have set for a pillar, shall be God's house: and of all that thou shalt give me I will surely give the tenth unto thee. Gen 28:22

So, the explanation goes, if Jacob counts backward from his youngest son, the 10th son is Levi. Thus, Levi is tithed to God in the priestly service.

Audrey's answer is correct, and here is the quote. The Levites remained loyal and restored order when the people were worshiping the Golden Calf. They killed 3,000 of their fellow Israelites, which set them apart.

19 When Moses approached the camp and saw the calf and the dancing, his anger burned and he threw the tablets out of his hands, breaking them to pieces at the foot of the mountain. 20 And he took the calf the people had made and burned it in the fire; then he ground it to powder, scattered it on the water and made the Israelites drink it.

21 He said to Aaron, “What did these people do to you, that you led them into such great sin?”

22 “Do not be angry, my lord,” Aaron answered. “You know how prone these people are to evil. 23 They said to me, ‘Make us gods who will go before us. As for this fellow Moses who brought us up out of Egypt, we don’t know what has happened to him.’ 24 So I told them, ‘Whoever has any gold jewelry, take it off.’ Then they gave me the gold, and I threw it into the fire, and out came this calf!”

25 Moses saw that the people were running wild and that Aaron had let them get out of control and so become a laughingstock to their enemies. 26 So he stood at the entrance to the camp and said, “Whoever is for the Lord, come to me.” And all the Levites rallied to him.

27 Then he said to them, “This is what the Lord, the God of Israel, says: ‘Each man strap a sword to his side. Go back and forth through the camp from one end to the other, each killing his brother and friend and neighbor.’” 28 The Levites did as Moses commanded, and that day about three thousand of the people died. 29 Then Moses said, “You have been set apart to the Lord today, for you were against your own sons and brothers, and he has blessed you this day.” (Exodus 32:19-29)

You are also correct about Genesis 49:5-7 being relevant. This was the time when their violence served the Lord, and the curse upon them was turned into blessing. They received no inheritance of land, but instead inherited the priesthood.