At around 20 Aragorn is told his ancestry and meets Arwen and is smitten by her. Over the 20 years or so he becomes a victorious Captain in both Rohan and Gondor. While in Lorien he then meets Arwen again. The fall in love and pledge themselves to one another. Elrond finds out and the next time he sees Aragorn tells him that the only Man (mortal) he will allow his daughter to marry is the king of the west.
I don't see anywhere that Aragorn wanted nothing to do with his parentage. If anything we is completely committing to becoming the King of the west if only to marry his love.
However, he seems to also be aware that victory over Sauron will not come through strength of arms. He does not have Narsil reforged into Anduril until the One ring is found. Did he come by this knowledge from his own time fighting against the forces of the enemy? From his close counsel with Gandalf? Both? We don't know for sure.
I find the character very compelling for many reasons, in no small part due to his doubts about himself, but nowhere do I see a rejection of his ancestry.
I'm not sure what your measure is for "rejecting his ancestry". I mean, clearly he never literally rejects his ancestry in either book or film - but he has doubts in both.
In the film, he doubts "the strength of men" and worries about whether he is up to the task of defeating Sauron and reclaiming his throne. It is Arwen who assures him that he is "not Isildur", and will be able to prevail.
In Appendix A, when he first tells Arwen who he is, "he felt that his high lineage, in which his heart had rejoiced, was now of little worth, and as nothing compared to her dignity and loveliness. . . . [and] Aragorn was abashed, for he saw the elven-light in her eyes and the wisdom of many days . . ." (The quotes are from pp 1095-96 of my Unwin one-volume edition.)
Later, in conversation with Elrond, the latter says that "she is of lineage greater than yours . . . She is too far above you." (p 1096) Elrond also tells Aragorn that "A great doom awaits you, either to rise above the height of al your fathers since the days of Elendil, or to fall into darkness with what is left of your kin." (p 1096). Aragorn does not dispute this, but rather "[takes] leave lovingly of Elrond" before setting out on nearly thirty years of errantry, and we are told that "His face was sad and stern because of the doom that was laid on him". (p 1097)
When he meets Arwen again, she tells him that "Dark is the Shadow, and yet my heart rejoices; for you, Estel, shall be among the great whose valour will destroy it"; but he replies with doubt, saying that "I cannot foresee it, and how it may come to pass is hidden from me. Yet with your hope I will hope." (p 1098)
Again, we see that Aragorn takes hope and assurance from Arwen, which assuages the doubts and doom that he feels within himself. He wants to be king, of course, and thereby realise his destiny and marry his beloved. But he has doubts that he will be able to do what is required.
In the film, we see Aragorn struggle more with the consequences for Arwen of their betrothal, but then we see more of their interactions full stop. But in Appendix A, when Aragorn is dying, he offers Arwen the opportunity of repentance - so even in that respect, the film is not wildly at odds with the book in trying to convey the consequences for Arwen of her choice, and the significance to Aragorn of that consequence.
In the book, it seems to me that the truly pivotal scene in which Aragorn's doubts (well-expressed in his lamenting that "An ill fate is one me this day, and all that I do goes amiss" (p 433)) are dispelled, and his confidence rises to match Arwen's hope, is his wresting of the Palantir from Sauron's control. This is where we see him transcend any need for advice from Gandalf, and assert his kinghood: "I am the lawful master of the Stone, and I had both the right and the strength to use it, or so I judged. The right cannot be doubted. The strength was enough - barely." (p 811) In the films I don't think the trajectory is wildly different, although the delivery of Anduril rather than the use of the Palantir serves as the pivotal event.
