Why did Sirius Black wanted to kill Harry Potter in the beginning?

When they were all inside the tree sirius black told the warewolf guy that he wanted to kill harry potter and the warewolf man gave him the wand so he can kill him, but why did he want to kill him then? because later he started being nice to harry and inviting him to come live with him, I dont understand why did he change from wanting to kill harry to protecting him?