Why did the Holy Family have to flee to Egypt?

Saint Joseph was ordered by an angel in a dream to take the Infant Jesus and His mother and flee to Egypt. They immediately did so, in obedience to God through His angel. We see this account in Matthew chapter 2.

Matthew 2: Now when [the Magi] had departed, behold, an angel of the Lord appeared to Joseph in a dream and said, “Rise, take the child and his mother, and flee to Egypt, and remain there till I tell you; for Herod is about to search for the child, to destroy him.” And he rose and took the child and his mother by night, and departed to Egypt, and remained there until the death of Herod. This was to fulfil what the Lord had spoken by the prophet, “Out of Egypt have I called my son.” …
[W]hen Herod died, behold, an angel of the Lord appeared in a dream to Joseph in Egypt, saying, “Rise, take the child and his mother, and go to the land of Israel, for those who sought the child’s life are dead.” And he rose and took the child and his mother, and went to the land of Israel. But when he heard that Archelaus reigned over Judea in place of his father Herod, he was afraid to go there, and being warned in a dream he withdrew to the district of Galilee. And he went and dwelt in a city called Nazareth, that what was spoken by the prophets might be fulfilled, “He shall be called a Nazarene.”