In the Yalkut Shim'oni on Ⅰ M'lachim 18 (remez 214), we see a bit more of the story found in that chapter of Navi:
Eliyahu's bull continued following him. But the bull that was designated for Baal — all 450 Baal prophets and 400 Ashera prophets gathered but could not move its feet from the earth.
So it was until Eliyahu spoke up and said to the bull, "Go with them."
The bull replied to Eliyahu in view of everyone, "My peer and I came from the same womb and were raised in the same pasture and from the same trough. He's apportioned to God and God's name will be sanctified through him, whereas I am apportioned to Baal to anger my creator!?"
Eliyahu told him, "Go with them; let them not find a complaint. And just as God's name is to be sanctified through this one that's with me, so will it be sanctified through you."
The bull said, "So you advise me? An oath: I will not budge from here until you pass me into their hands."
Immediately, [Eliyahu did so, as verse 26 says,] "They took the bull he'd given them" — who'd given it to them? Eliyahu.
If Eliyahu's argument convinced the bull, then why did it require Eliyahu to hand it over? If, alternatively, the argument didn't convince it, then why would Eliyahu's handing it over help any, that it allowed itself to be offered to Baal on that condition?