My flight times are contradicting? Departure, arrival, and duration do not make sense!?

You're changing time zones

All times listed are local to the airport you arrive or depart from.

For example, if you were flying from NY to LA, you would take off at 9:15pm Eastern Time, are in the air for 4 hours, and then land at 11:27 PM Pacific Time. The time from your departing airport would be 2:27am, but you're not in that time zone anymore.

Do you move across time zones?

Arrival and departure times are local times

You are crossing time zones. Departure and arrival times are local, meaning it will be 9:15 pm in your departure city when you leave and it will be 11:27 pm in your arrival city when you land.

Departure and arrival times are the local time at each airport. The duration seems off because you haven't accounted for the time zone difference

And if you are in America this Sat. night is the time change. That may or may not be a factor too.

The departure and arrival time is always given in local time. You are flying to a city that's one hour behind your time zone.

Don't feel bad. When I was in college I worked at a travel agency; this was before Internet. We had a client doing one of those seven cities in five days business trips. One flight was from Grand Rapids, MI to Chicago. The scheduled flight time is 45 minutes, but Chicago is in the Central time zone while Michigan is in Eastern. So his itinerary looked like he would arrive in Chicago 15 minutes before he left Grand Rapids. Took me almost an hour to explain that one to him, and I am still not convinced that he fully understood it. And he looked like a smart guy.

You forgot about TIME ZONES.

It makes total sense if you are flying 2 time zones west. Which I don't know because you forgot to say WHERE you are flying from and to. But with a 4 hour flight, covering 2 zones looks very possible.

Of course you are missing something - the time zone difference. Flight times are always given in local time to avoid confusion with planning when you need to get to the airport, and planning what to do after you arrive. So it's 9.15 pm where you are when you leave, and 11.27 pm where you are when you arrive. With a flight time of 4 h 12 min, obviously arrival time is 1.27 am where you started - BUT YOU'RE NOT THERE NOW! So this is a useless thing to know. Where you are after landing is in another time zone where it's 2 hours earlier, 11.27 pm. So you will have to wind your watch back 2 hours to put it right. Surely Americans know about time zones? You've got 4 of them just in the continental USA.

If that's confusing you, imagine what a longer flight is like - you'll certainly know then. A friend and I flew from London, England, to San Francisco. That takes 11 hours but it's 8 time zones away so we apparently landed only 3 hours after we left. It was 6 pm in SF but 2 am next day by our body clocks - you bet we were feeling totally zonked and all we wanted was BED, lovely BED... Now guess who was first in the hotel restaurant for breakfast next morning?

Going the other way is even madder. That's 11 hours PLUS 8 hours time difference and flights are normally overnight Let's say it departs at 4 pm, then it will arrive in London at 11 am local time next day with your body thinking it's still only 3 am. The zonked feeling of jet lag is indescribable and if you can't get some sleep on the flight it only gets even worse - which is why my friend booked us into premium economy. I'm tall and he thought a few inches extra legroom would help me snooze, which it did.

You depart at 9:15Pm local time, you arrive at 11:27PM their time or 1:27AM your time. Now isn't that possible? You must not fly very much as a person that fly would know this.

Time zone is the answer.

You are missing crossing from one time zone into another.Departure and arrival times are posted in local times.
You could leave Cincinnati at 6))Pm and arrive in ST Louis at 600PM..the reason, Cincinnati is Eastern Standard time and St Louis is Central standard time

Yes, your flight times might be contradicting and you must be getting confused regarding your departure, arrival and duration. This makes sense particularly when you are flying 2 time zones west in the United States. Even a 4 hour flight can cover 2 time zones. Remember that flight times are always displayed in local time for avoiding confusion. It possibly seems that you are perhaps travelling for the first time within the USA and aren’t aware about the different time zones in the country as much as Americans do. There are in fact 4 time zones just in the continental USA.

What cities
There are 4 different time zones in Conus, sounds like you are leaving one and flying west going to thee one that's 2 hours earlier then the one you left.
Example leaving the Central Timezone and going to Pacific or leaving Eastern and going to Mountain