This account is a warning: don’t make foolish vows. They don’t bribe God to do anything He wouldn’t have done anyway, and they could cost you something you really don’t want to lose.
11:30-31 And Jephthah made a vow to the Lord. He said, ‘If you give me victory over the Ammonites, I will give to the Lord whatever comes out of my house to meet me when I return in triumph. I will sacrifice it as a burnt offering.’
God was probably going to grant victory anyway. All Jephthah did in this vow was to inadvertently promise away his only child as it was she who came out of the house to meet him.
You can be sure that Jephthah had a ‘what’ in mind, such as an animal, when he made the vow, not a ‘who’. Could he have argued the point with God? Shakespeare would have (Macduff’s victory in Macbeth), as would have Tolkein (Éowyn’s victory in the Lord of the Rings), or any of the legion of bureaucrats and politicians we have these days.
But Jephthah wasn’t the sort to argue over words. His was a simpler view of life, and he responded in grief:
11:35: When he saw her, he tore his clothes in anguish. ‘Oh, my daughter!’ he cried out. ‘You have completely destroyed me! You’ve brought disaster on me! For I have made a vow to the Lord, and I cannot take it back.’
Jephthah couldn’t offer a female (human or animal) in this way: only male animals were acceptable as burnt offerings. He would have known that. He also wouldn’t have been able to find a priest to do it for him. Human sacrifice was strictly forbidden.
Unless Jephthah was expecting his dog to bound out of the house first, and a dog wasn’t acceptable as a burnt offering anyway, it’s more likely that he was thinking along the lines of a vow he couldn’t take back.
Perhaps Jephthah’s grief was not over the imminent death of his daughter, but over his own loss of her from his household.