In Judges chapter 11, we get a story of a man named Jephthah. His story is often construed by Atheists or other critics of the Bible as God demanding human sacrifice.
Jephthah made an unnecessary, unsolicited, and foolish vow that if God helped him to defeat the Ammonites in battle, that he would offer as a burnt offering the first thing that came out of his house when he returned home:
Judges 11:30-31
30 And Jephthah vowed a vow unto the Lord, and said, If thou shalt without fail deliver the children of Ammon into mine hands,
31 Then it shall be, that whatsoever cometh forth of the doors of my house to meet me, when I return in peace from the children of Ammon, shall surely be the Lord's, and I will offer it up for a burnt offering.
However, when he returns, his daughter is the first to meet him:
Judges 11:34-35
34 And Jephthah came to Mizpeh unto his house, and, behold, his daughter came out to meet him with timbrels and with dances: and she was his only child; beside her he had neither son nor daughter.
35 And it came to pass, when he saw her, that he rent his clothes, and said, Alas, my daughter! thou hast brought me very low, and thou art one of them that trouble me: for I have opened my mouth unto the Lord, and I cannot go back.
He later kills her and offers her as a burnt offering to God, fulfilling his oath.
"Well, He didn't prevent it, therefore He approved of it, right?" No - how many murders happen every day? That's a foolish argument. God, as a general rule, allows humans to operate under their own free will so that our choices actually have meaning. If your hand stopped working every time you went to sin, you wouldn't have free will.
The blame falls squarely on Jephthah. I see four ways that he could've avoided killing his daughter:
The fact is, even if God was to kill Jephthah for breaking his vow, he's still trading his daughter's life for his. Even more selfishly - if God did less than kill Jephthah, he's trading her life for some temporary curse from God. If I had already made his mistake, I would've tried option #2 or #3, as it's likely God wouldn't kill him, and the only other option is taking a life.
In regard to the fourth option, there was specific provision in the Mosaic Law for redeeming the price of a person that had been vowed in service to the Lord. For Jephthah's daughter, this would be 30 shekels:
Leviticus 27:2, 4
2 Speak unto the children of Israel, and say unto them, When a man shall make a singular vow, the persons shall be for the Lord by thy estimation.
4 And if it be a female, then thy estimation shall be thirty shekels.
Of course, note that this wasn't for people who had been promised to be sacrificed as a burnt offering, because such a thing was never supposed to happen. However, I would've tried this anyway due to the fact that it has to do with redeeming someone vowed to the Lord, which technically would apply to Jephthah's case.
In no sense does God ever support human sacrifice - as He explicitly condemns it multiple times (Leviticus 18:21, 20:2, Deuteronomy 12:31, 18:10, Jeremiah 7:31, 32:35, Ezekiel 16:20-21, 20:31, etc.) - and in no sense did Jephthah have to kill his daughter. This is a cautionary tale about flippant oaths (especially unsolicited flippant oaths).