One possible motive could be ransom. The kidnappers may think the girl's family is wealthy and they can get a large sum of money in exchange for her safe return.
Another motive might be revenge. Maybe the kidnapper has a grudge against the girl's family. For example, if the family member of the kidnapper was wronged by the girl's family in the past, they might kidnap the girl to get back at them.
Love or obsession could be a motive. Just like in some stories where a girl is so in love with a boy that she kidnaps him thinking it's a way to keep him close.
Another motive could be revenge against the girl's family. Maybe the kidnapper has a grudge against her parents or relatives. Gagging the girl is a way to keep her quiet while they carry out their plan of getting back at the family in some way.
A possible motive could be revenge. Some characters who have a grudge against Lupin, perhaps because of his association with certain groups or events in the wizarding world, might kidnap him. For example, if a werewolf-hating group found out his identity, they could kidnap him to make an example out of him.
One possible motive could be a desire for friendship. Maybe one girl sees qualities in the other that she admires and wants to be close to her, like in the case where one girl is attracted to the other's creativity and tries to 'seduce' her into a friendship by sharing related interests.
In the 'girl in basement' real story, there are several possible motives. Financial gain can be one, where the captor may be planning to ask for ransom from the girl's family. Another motive could be isolation and experimentation. Some captors may be interested in seeing how the girl will react to long - term isolation and may conduct cruel 'experiments' on her mental state. Additionally, there could be motives related to jealousy or envy if the captor has an unhealthy fixation on the girl's life or appearance.
One possible motive could be Bellatrix's loyalty to Voldemort. She might think that by kidnapping Hermione, she can get information about Harry Potter and the Order of the Phoenix. Hermione is known to be very intelligent and Bellatrix could believe she has valuable knowledge. For example, Hermione might know the location of Potter or the Order's plans against Voldemort.
One possible motive could be to use Hermione as a bargaining chip against Harry Potter. Since Hermione is his close friend, the kidnappers might think they can force Harry to do something, like give up a powerful magical item or valuable information.
The girl might just want attention. Sitters are often there to take care of her, and by 'seduce' in a cute way, like sharing her toys or stories, she can ensure that the sitter focuses on her more.
One possible motive could be financial gain. Older men are often more financially stable, and the girl might see an opportunity to have a more comfortable life. Another motive could be a search for father - like figures. If she lacks a proper father figure in her life, she may be attracted to the older man's maturity and stability.
Another motive could be coercion. Maybe she was part of a gang or some sort of criminal group that forced her to kill. They could have threatened her or her family if she didn't comply. Or perhaps she was in a situation where she thought killing was the only way to protect someone she cared about. For example, if she was in a war - torn area or a place full of violence, and she believed that by killing a particular person, she could save her friends or family from harm.