I would focus on the distinction between the word "flight," which they use in their letter, and "trip," which is what the coverage discusses. Your card doesn't offer "Flight Delay Protection" but "Trip Delay Protection." The card's terms define Trip as "any pre-paid travel, tour or vacation when all or at least a portion of the cost of the Common Carrier fare was paid using your Citi card and/or ThankYouŽ Points for all Covered Travelers." You didn't purchase a Common Carrier fare for XXX-YYY (the first leg of your trip), you purchased a fare for XXX-ZZZ with a change of planes in YYY (this part of the argument is harder if your plane ticket's fare construction is actually a combination of two fares, but the odds of that are low). Because of weather (a covered condition) you were delayed more than 3 hours in reaching your final destination; therefore your Trip was delayed more than 3 hours even if the first flight in your Trip was only delayed 1.5 hours.
If you really want to fight hard, you might cc the insurance regulator in the state where you live in your response..