Snape overheard a part of the prophecy-predicting what the person who defeated Voldemort would have-Voldemort knew the prophecy-and according to the prophecy, he found two candidates (Harry Neville)-Neville is like a dumb gun, and Harry is of muggle descent, much like Voldemort-so Voldemort chose Harry and thought that Harry would pose a threat to himself.
Voldemort is ruthless, and it is not difficult to kill a person. He did a lot of bad things himself. At this time, his soul split and his judgment dropped sharply.
As for later, everyone knows that Harry Potter defeated Voldemort. Can Voldemort stand it? Can't get the venue back? Besides, it is normal to create drama and conflict in novels.