First of all I'd like to thank you for the answer. But to be honest...
Unofrtunately I don't.
I was always told that we use the present perfect tense to talk about things which affect "present", but took place in the past. As in your example (the first one) - my flight was delayed (in the past) and right now I'm late (in the moment of speaking with friend - present) - so why wouldn't I use the present perfect tense there?
1. You arrive at the arrivals gate at the airport, your friend is there to meet you, you say: "I'm sorry I'm so late, my flight got/was delayed".
2. You phone your friend from the departure lounge, you say: "My flight has been delayed so I'm going to be late".
In #1, The fact of your flight being delayed is in the past, it's finished, it is not delayed now.
In #2 your flight is still delayed, you haven't yet been able to board the plane.