I'm sorry, but that's really bad advice. I wouldn't say healers are "required" to DPS, but this game's content is not centered around you healing full time, ESPECIALLY Scholar. I've seen healers that throw a Cure/Physic/Benefic every time a tank falls below 100% HP and it's one of the biggest ways to seem like you're working hard but accomplishing very little. Sure, you'll get those tanks every once in a while who insist that they're DPS and don't pop a single cooldown and you'll end up on babysitting them, but this isn't usually the norm.
Again, it's not that you're required to DPS, but when you're just standing there, doing absolutely nothing, why wouldn't you want to contribute to the group? This falls into the whole "doing the bare minimum" argument. Suppose you roll as a SCH and you get Toto-rak or anything below it for your leveling roulette. I'm not even joking when I say that you can take out Eos, auto-follow your tank, and complete the dungeon, but do you honestly think that makes you a contributor to your team? As someone brought up earlier in this topic. You can be a tank, Overpower spam, Flash, or Unleash/Abyssal Drain in an AoE pull, then go AFK. You CAN do that, but it's just lazy, and same goes for healers.
My advice would be to start getting used to DPSing as soon as you feel comfortable healing. Low level dungeons require VERY little healing, and give you a lot of time to DPS as a healer. The earlier you start getting comfortable with cleric dancing, the easier it will be in the long run. The longer you hold out on it, the harder it will be to get used to. You'll have a much easier time learning how to cleric dance in anything from 1-39, rather than starting at Stone Vigil, or Aurumn Vale. Healing is not so much about knowing when to heal as to knowing when not to heall.
OP, the game has 3 healing jobs. Out of all of them, SCH is the most DPS-intensive, has the more complex DPS toolkit out of the other 2 healers, and has a Fairy that will help you heal. If you don't prefer to DPS, you might not like SCH. Astros are a cool mix of healing/support, and if you enjoy being busy all the time, I think you'll enjoy that job. WHM is the current king of burst heals, and their DPS capabilities fall between SCH and Astro, Astro being last.
You're by no means required to DPS, but it's a nice thing you can do to help out a run go faster (you'd be surprised at how faster a run will go when your healer DPS'es), or just for the sake of doing something when you have no heals to throw it (because overhealing is a bad thing and you shouldn't get used to it). Also, it's a good idea to keep in mind that DPS can be its own sort of mitigation, because you're killing things faster.
As a sidenote, tanks, especially WAR's and DRK's, have self-sustaining abilities themselves. Unless your tank is very squishy, or you're doing a fight that involves a tank buster, it's a good idea to start healing a tank roughly at 50-60% HP instead of every time they fall below 100%. The reason for this is that they can recover the HP you're trying to heal by themselves. For example, at a level 60 expert roulette, if I roll as a DRK or a WAR, for boss battles, the only healing I will need will come from your Eos. Any healing done by you will be completely unnecessary, because Eos/Selene and Souleater, or Inner Beast, Bloodbath+IR+Berserk, Storm's Path, Equillibrium, and Thrill of Battle are more than enough to keep me alive.