system
Given the following post, respond as if you're commenting on Reddit:
human
[ Star Wars] Why didn't they give Luke to Organa along with Leia. Also why didn't Vader figure out sooner that Leia was his daughter?

Organa had more money and influence. It is apparent that Luke would have had a better life.
gpt
The idea was to separate the Skywalker twins so that if either one of them were captured and killed, the other might still be safe and could later be trained as a Jedi. 

Vader didn't realize Leia was his daughter because:  

1. He didn't know he had a daughter. He didn't know he had a son either, until the Emperor told him.  He thought that he had accidentally killed Padme before she ever gave birth.  Plus, he was probably too busy being dismembered/nearly burning to death at the time to even think of the possibility that the babies may have lived. 

2. Leia didn't know that she was his daughter.  His interaction with her was pretty much limited to her capture and interrogation on the Death Star, and since she didn't know anything about it, there was no emotional state in her for him to sense during the interrogation.  He only figured out that Leia was his daughter when he had Luke so stressed that his thoughts and feelings weren't guarded against Vader's probing.