CRAWFORD: Your instructors tell me you're doing well. Top quarter of your class.
The reason Jack Crawford selects Clarice for the job is because she did well in her classes. The moral of this story, kids: do well in school, and maybe you'll be used as bait for a serial killer, too!
LECTER: Jack Crawford sent a trainee to me? […] Jack Crawford must be very busy indeed if he's recruiting help from the student body.
Jack Crawford has seen how promising Clarice can be. Hannibal Lecter has not. Clarice has to earn his respect. She had to earn Crawford's respect too, but that happened before the movie started. Lecter sees the situation as disrespectful to him—he probably thinks he deserves their most experienced agent.
LECTER: I will make you happy. I'll give you a chance for what you love most. […] Advancement, of course.
Hannibal Lecter recognizes how ambitious Clarice is. She earns his respect during their interview with her candor, and in return, he wants to help her earn respect from others.
CRAWFORD: Starling, we wouldn't have found him without you. Nobody's gonna forget that. Least of all me.
Clarice wants to impress Jack Crawford because he's like a father figure to her. Lecter is, too, in a way, but Crawford is a person Clarice can actually look up to. Their relationship is not romantic, despite what Lecter suggests earlier.
CRAWFORD: Your father would have been proud today.
This is one of the last things Jack Crawford says to Clarice in the movie, giving her exactly what she wanted for the whole movie: respect from her father. But her father is dead, so this surrogate father will just have to work.