From the text quoted in this answer, I got the answer finally.
Like how we are mistaken to equate "killing = violence" due to its nature, we often mistaken "correct information" as "truth" and "incorrect information" as "falsehood". But Krishna clarifies it to be "utter-able" and "unutterable" respectively:
Behold, however, truth as practised is exceedingly difficult to be
understood as regards its essential attributes.
Truth may be unutterable, and even falsehood may be utterable
where falsehood would become truth and truth would become falsehood.
Had Yudhishtira told Drona about his son was not dead, then he would have just given the "correct information" like a machine. After that Drona would have killed the whole army of PAndavas. In such case a side will be victorious, which subscribed to treachery (dice game), murdering (LAkshAgriha), molestation (Draupadi's insult), renege (denying kingdom after 13 years). This would have caused deterioration in the society under such regime.
Suppose, you have a high standard of taste being a restaurant owner. A relative invites you for a meal with compassion and feeds you terrible food. If asked, "How was the food?", would you say: "Terrible"?
No! "Terrible" is just a correct information, which describes the food. But "dinner invitation" is not limited to food alone, it involves the "compassion" as well. In such case, you may want to lower your standard for "food" and say it was "Good"!
Above also doesn't mean that, you should blindly follow others' emotion beyond threshold. If the other person expresses an interest to become the chief cook in your restaurant business, then ofcourse your priority will change from "saving emotions" to "saving jobs"! :-) In such case "correct information" becomes "truth".
Some patients are not informed the computer generated "correct report" that he/she has cancer. That's Not falsehood, because if told it may create distress on sensitive person. Rather his/her relatives by saying "everything is OK", allows the patient to live a less stressful life. That becomes the "Truth".
In general, "truth" is not limited to information, but also how broad purpose it serves. We need to have discrimination, that we are not using "incorrect information" for limited/selfish purpose.
"... why women and marriages are covered?"
This seems just an example, where you may have to often practice differentiation of "truth" vs "correct information". That is explained in subsequent para:
On an occasion of marriage, or of enjoying a woman, or when life is in danger, or when one's entire property is about to be taken away, or for the sake of a BrAhmana, falsehood may be uttered.