Just from my experiences:
1.) Healing isn’t rewarding. If things go good in a raid, the DPS with the biggest bar gets the credit. If things go good in a party, the Tank gets thanked. If things go bad in either place, Healers get blamed.
2.) Healing progression is not nearly as noticable as Tank/DPS. If your a geared tank, you know it and can tank half an instance. If your a DPS, you blow things up and the meter is as long as you can make it. If you’re a geared healer? Things don’t die harder? Or it’s easier to heal snipe. I don’t really know… outside of fights where everyone’s always at half life no matter how hard you heal, I don’t see the point.
3.) Healing doesn’t translate into solo play. Oh you’re a healer? Cool. Get blown up in BGs. Tanks can at least do comically impossible large pulls that most DPS can’t so there’s some parody there. Screw off trying to solo anything efficiently. Better group or change to a DPS spec.