。
She wasn't keen on revealing her secret.
Literal
She [topic-は] her own secret [object-を] reveal [thing-こと-に topic/contrast-は] mind [subject-が] was-not-advancing.
気が進まない (literally 'one's 気 — mind, will, inclination — does not advance') is the idiomatic way to say 'reluctant, not in the mood for, unwilling to.' The construction nominalizes the action with ~ことに, then attaches contrastive は (~ことには) to topicalize 'as for revealing her secret.' 明かす ('to reveal, divulge, disclose') pairs naturally with 秘密. The past 進まなかった makes this a one-time past attitude rather than a habitual one.