Holy Priest, what am I doing wrong?

What I am wondering about is: why are they questioning you? Are you experiencing frequent deaths and wipes due to low healing in your raids? Because if you don't, why bother about HPS and Healing done (by the way, did you check overhealing?). This answer might be highly subjective but I really think that not high numbers make a good healer, but knowing whom to heal when. As long as your raid performs well and you never seem to be lacking heals, you shouldn't worry too much.

Concerning the topic of "the other healers are healing faster" - in case you use Healbot, this might be the cause, since it lags a bit in displaying HP. Grid would be a very nice alternative that can also show you which targets are expecting an incoming heal from other healers.

Your gearing and gemming seems fine, minus a few things I would personally change. Your spec is fairly standard.

The only thing that is unknown is: what spells are you using. (world of logs is exceptionally helpful)You should NOT be using Flash Heal in that gear. Your renews will outpace it notably. --- even with SOL procs. I only use SoL procs if I need a heal on someone for a decent amount NOW, vs a lot more over time with Renew-- or to keep up my Serendipity so I have it banked when I need to POH.

I also suggest posing this question in the Priest Forums over at Plus Heal. Thereare a lot of folks there who can provide additional insight.

Have you tried Healbot? Personally it improved my healing thousand fold.

Healium is my favorite, I have tried them all, and Healium seems to be the best for my Holy Priest...