A typical activity in a biology class is to dissect a frog. So the speakers are making frog jokes.
The girl's line is a pun on the word riveting (fascinating, attention-grabbing - something that holds your attention as if it were fastened with rivets) and ribbit (an onomatopoeic word for the croaking sound made by a frog).
The quote marks serve to indicate that the speaker is placing extra emphasis on the word ribbiting, to call attention to her joke.
The boy is using the set phrase leap to conclusions (to make a decision about something based on insufficient evidence, also commonly worded jump to conclusions), but emphasizing the word leap, because leaping is something that frogs do. Here the joke involves the double meaning between the figurative and literal senses of leap.
The phrase Kermit suicide mentioned in comments is another pun: on commit suicide (to kill oneself) and Kermit the Frog, a well-known fictional character.