In the beginning Frederick’s failure to reapply to Anne after he was made clearly tells her that he is no longer interested. As nonverbal signals go is not eight years of silence the greatest cold shoulder of all? Anne was observant of all the intelligence she could find out about Frederick. His behavior does not dispel the notion of his disinterest. He must have known of Anne’s presence at Uppercross from his sister yet he did not enquire of her when Mr. Musgrove visited him (7) as anyone might of a common acquaintance or when he returned the visit (7). At the first dinner Anne avoids he finally inquires about her “slightly, as might suit a former slight acquaintance” (7) and Anne reasons with the hope she shares of “escaping introduction when they were to meet” (7). An introduction would require them to converse and he seems to want to avoid it as much as she. If Anne’s failing to speak to him after curtseying is a cold shoulder then she is only doing what she believes he desires as much as she.

He had not forgiven Anne Elliot. She had used him ill, deserted and disappointed him; and worse, she had shewn a feebleness of character in doing so, which his own decided, confident temper could not endure. She had given him up to oblige others. It had been the effect of over-persuasion. It had been weakness and timidity. (7)

As you did not specify I suppose the violent dislike of Anne referred to is my interpretation of Frederick’s speech in Ch. 8? I disagree we know nothing of his motives. Recall we are told of his feelings and opinions (above) and they suggest all the motivation needed to explain his behavior towards Anne. He has not forgiven her for “so forced a relinquishment” (4) and from that it is reasonable to deduce he is still angry and resentful. The fact he cannot endure Anne’s so called feebleness of character speaks of contempt. Anger, resentment, disappointment and even contempt are known motivators. I think what JA is showing us in Frederick’s performance at the pianoforte is a very natural, common reaction to rejection and disappointment. His behavior is colored with contempt, angry pride and resentment arising from strong feelings of ill use and disappointment. It is reminiscent of other rejected suitors in The Novels who feel their full share of ill use at the whims of a lady. Mr. Collins after Lizzy refused his offer:

As for the gentleman himself, his feelings were chiefly expressed, not by embarrassment or dejection, or by trying to avoid her, but by stiffness of manner and resentful silence. He scarcely ever spoke to her… (P&P, 21)

Mr. Elton after Emma refused his offer:

He was too angry to say another word…and in this state of swelling resentment, and mutually deep mortification…The compliment was just returned, coldly and proudly; and, under indescribable irritation of spirits… (E, 15)

Frederick’s behavior is technically correct but it is my experience people can and do express their negative feelings under cover of correct behavior. For example Miss Bingley’s “kindly meant” (18) revelations about Wickham in P&P. No one but Jane could believe she meant any kindness to Lizzy whom she dislikes and views as a rival. She probably hoped to give Lizzy some pain by ruining her favorite. Similarly, I can’t imagine Frederick thought his studied politeness, pointed speech and “such unnecessary, such officious attention” (P&P, 53) was the disinterested courtesy it appeared. There is no true politeness in the attention; it is a cold dismissal of the lady who injured him. Insisting the seat at the pianoforte belongs exclusively to Anne only serves to breakup the party at the instrument and discomposes Anne. I do hope to give relief by confessing that I do not see Miss Bingley’s calculated mean-spiritedness in Frederick. I think he can’t resist the impulse to convey his feelings in the passive aggressive style described above. I like to believe Frederick was thoughtless rather than cruel; too wrapped up in his own feelings to perceive dear Anne’s.

Frederick had “never seen a woman since whom he thought her equal” (7) so I do believe there is lingering admiration for the girl he previously thought Anne to be. I doubt not the memories are painful and his feelings strong. I think his wish to avoid Anne is natural considering the provocation of their broken engagement and the fact this is their first meeting in eight years. I disagree that Anne’s motives for avoiding Frederick are irrelevant. So far each of Anne’s so called “cold shoulders” to Frederick can be traced to her attention to his wishes as well as her own. She follows his lead from the start. I don’t think this is justifying Anne’s avoidance at Frederick’s expense rather I am saying her behavior is the natural consequence of his—well, except, I think she is angelically understanding of his feelings and opinions about herself.