Hi LiJ I don't know what the natives think but to my mind it's not a good idea to have idea as an object of feel . I don't think one can "feel an idea". In is the wrong preposition in your sentence.
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Cool BreezeAt this time of the year people might/could subscribe most strongly to the idea that time flies.I understand yours is the best.
LiveinjapanHow about this?It's correct English but "to feel strongly about" doesn't have the meaning of "subscribe to", which in your sentence means more or less the same as "agree with". You could say, for example: He feels very strongly about human rights. (= Hum
At this time of year people might feel most strongly about the idea that time flies.