The support rep on the phone didn’t break your order. Talk to them like a human who’s on hour seven.

Whoever answers the phone did not cause the problem and cannot leave the conversation. Venting at them successfully makes the moment worse for one person with no stake in what went wrong. Treating them as a person also tends to get you better help, though that is not really why to do it. The frustration is legitimate; the target is not.

Open by saying you know this is not their fault. Describe the problem once, clearly, and then let them work. Thank them by name at the end.