Yep, you have your points and they are valid, do not let your other half tell you otherwise. However if you look at it from their side, are you over reacting? Have you acted a bit hastily in hanging up the phone? When you see it from their point of view; was the way they acted not reasonable within the situation. Ask these questions before you create world war three and see if you can resolve it.
If they're the ones in a different place to what they where used to (meaning the one who had moved and is living long distance) is there stuff going on to make them behave in the way they are. Could there be reasons behind the argument that need to be unfolded? If so work them out amicably because arguments just make life twice as hard as it needs to be.
3. Be The Bigger Person
Have you argued the same point over and over again for hours or even days? Do you think you can be the bigger person and bring positivity to the relationship by sending the first ' I Love You' text after an argument or the first 'I'm Sorry'. Could you resolve it by getting over you acute stubbornness, If so, surely it's worth the hit to your pride.
4. Forgive and REALLY Forget
Do not bring the same issue up in every argument, if you have both apologised, you need to let it go. As having the same underlying issue in every argument, especially in long distance can become the monster that destroys you.
5. Ultimate Point
Remember why your long distance in the first place , you wanted it to work, so make it work!
Most importantly check if it can be resolved, before everything blows up between the two of you.