I DPS not because healers are able to DPS, but because healers are able to heal so very well. Healers are packed with powerful abilities that allow them to restore large amounts of HP quickly, and a lot of those abilities simply aren't necessary when people are playing well in everyday content and not making mistakes. DPS healers basically simulate large amounts of incoming damage by allowing damage to accumulate on the tank during a window they choose to DPS, then bursting them back up with powerful restorative abilities that would otherwise sit unused.

DPS healers are calculated risk takers that, ideally, calculate correctly every time. It's less about how much DPS you can push and more about how much time you can buy yourself to DPS. It's first more important to ensure everyone stays on their feet while you aren't attending to them before you worry about numbers. By understanding all of your abilities, your teammates' abilities, enemy abilities, and accounting for just the right amount of fault tolerance, you'll come to know your party's limitations, and this is simply experience gained over time, experiencing wide arrays of skill levels, party interactions, and unforeseen variables. You'll be able to apply the minimum amount of healing necessary, at a maximum throughput, leaving plenty of time for that DPS.

And yet, some players simply aren't interested in that optimized level of play, some aren't experienced enough, confident enough, they're learning their jobs, and yes, some players are even lazy. It's easy for me to say why I DPS, it's easy for someone else to say why not. There are simply too many unknowns when it comes to healer DPS to give one sweeping answer, both on your side of the screen and the other. Healer DPS isn't designed to be required, and yet, whether or not it's supplied, expected, or even welcomed varies from player to player, instance to instance. Play the class to what makes you content, but keep an open mind. There's always a way for you to heal more in less time, and the better you get at it, the more cushion your windows will have, and the more comfortable you can become shouldering responsibility outside the healing role.