Is a man sinful if he leaves a girl he was on the verge of marrying after a period of attachment and dating, due to family opposition, and then he is suddenly overcome by a feeling of disinterest in her? And is it permissible for him to lie to her that his family is the reason for his backing out to avoid hurting her feelings?

Fulfilling a promise is commendable, but it is not obligatory. There is no blame in withdrawing from a promise to propose to a girl for several reasons: that what occurred was merely a promise, that the family opposes the engagement, and a current lack of desire for her, which would make the marriage vulnerable to failure. The withdrawal does not require fabricating a false excuse; rather, mentioning the family's opposition as a reason is sufficient. The relationship with the girl must be severed.