Lizzie Schofield is quoting from John 10:18 to try and show Jesus wanted to be the sacrifice in the crucifixion narrative. The problem here is simple. She does not cite the verse in full. If she did, she would notice the last sentence of the verse could argue against her. Whether she deliberately avoided the last sentence in the verse is not clear.
The last sentence of the verse tells her, it is the Father’s will for Jesus to do be crucified. Jesus is complying with the Father’s will.
Lizzie’s interpretation would also contradict Matthew 26:39 where Jesus is praying to God (the Father) asking God to save him. This verse and verse 42 of the same chapter both state it’s the Father’s will.
If Jesus complies with the Father’s will, it’s still ultimately the Father’s will. At one point in the story, Jesus asked the Father to save him from crucifixion.
This is a big problem with Speakers Corner dialogues, people can partially and misquote on camera without being called out as the conversations are so fluid and fast paced.