Why are they angry or upset (or both)?
Is it because;
Lower educated/less literate
Vulnerable
Arrogant
Had 'smart' businesses take advantage of them
Think they're immune to normal expectations
Had their baser instincts (greed or vanity) appealed to
Confused
Didn't understand what they were taking on/getting into
Used to shouting getting them their own way
Have contempt for people over the phone
Upset because they've been pissed around, lied to, ignored and generally gone through it to get to the point of talking to you
Are dealing with an organisation (yours) that isn't up to scratch either
Have illnesses, job losses, other stresses in their lives that are coming out because this is the last straw for them
Are just desperate for help and feel you don't care
Is this life or death situations, losing homes, bereavements, huge stressful losses
?
Are they swearing at you or are they swearing whilst speaking to you? There's a world of difference when you're speaking with upset people.
Turning to you, do you interpret any stress in somebody's voice as being directed specifically at you, when it might not be? Do you need to develop listening skills, calm understanding of them being upset/frustrated/angry, boundaries in knowing exactly when you can terminate a call? Are you feeling supported by management and your colleagues?
When it comes down to it, there are myriad reasons why people get angry or upset during phone calls. Some, it's not really surprising because of what they've experienced either directly or indirectly. And some are just dicks in every aspect of their lives. You're just a voice on the phone - and could be the first person that has actually stopped to hear what they have to say, to explain the process, to give them an understanding, perhaps some sympathy, perhaps just to be there as their emotions spill over (within reason).
When it comes down to it, you're being paid to not be them. They're unhappy - and likely for good reasons (although not always), whether they're entitled to refunds/compensation or not - you can put your headset down at the end of the day and go home. You don't have their lives, the ones where they are so unhappy, for whatever reason.
It's business. It's not personal - you can choose to make them feel it's personal by explaining, by listening, by letting them feel heard. You can't make them all happy, that's not your job. But there will be people you can actually help in those calls if you manage to distance yourself from what can feel like a personal attack when it's actually raging at the world and hurting, remember your skills, your knowledge and abilities. For want of better words, professional detachment, professional sympathy, professional boundaries. You can be kind, you can be nice, you can be firm and assertive where needed. You can be professional. Because it's business. And you're being paid to do this.
You can do it.