To answer this question we first need to differentiate between seduction and rape. We also need to differentiate between pgam (loss of value) and boshes (shame) on the one hand, and tzar (pain) on the other.
With respect to seduction, the Gemara in Kesubos 42a says that the damages must go to her father because by definition she was mochel on pgam and boshes (there is no tzar).
לאביה איצטריך ליה לאביה נמי פשיטא מדקא יהיב מפתה דאי לעצמה אמאי יהיב מפתה מדעתה עבד
With respect to rape, the Gemara in Kesubos 40b says that her father gets boshes and pgam because since she is a minor (if she is older than 12 and half she gets everything) her father could marry off to whomever he wants, even a menuval or or a person with boils.
אלא מסתברא דאביה הוי דאי בעי מסר לה למנוול ומוכה שחין
Therefore, the only question remaining is tzar with respect to rape. Why does the father get the cost of her pain?
In fact, the Raavad disagrees with the Rambam and holds that the father does not get the cost of tzar with respect to rape, but only boshes and pgam.
What is the explanation for the Rambam (Rashi also holds this way) and the Ramah? I am not sure.
The Tosefos Yom Tov on the first mishna in the fourth perek of Kesubos brings an explanation from the Ran, that applies the Kesubos 40b reasoning to tzar also.
אע"ג דבפרק החובל אמרינן דצערא דגופה לא זכי ליה רחמנא [וכמו שאכתוב ברפ"ו לקמן] שאני האי צער שבידו לצערה כהאי גוונא דאי בעי מסר לה למנוול ומוכה שחין שנבעלת לו בעל כרחה ומצערת
But I don't know how this fits with the halacha that a man is not allowed to rape his wife.