If you want to contribute to your party and bring your job to it's full potential in this game, you need to DPS, therefore, healers are required to DPS to be a good healer. Summoners and Red Mages aren't REQUIRED to ress people, Bards weren't REQUIRED to give tp/mp before ShB, yet those that refuse to do that are seen as players that are just playing bad. If you refuse to DPS you're being a bad player. So it's not surprising that people will expect you to play your best.
I absolutely adore Yoshi-P, but his views towards healing clearly do not show how healing really works in the game, and we can see how the team also doesn't understand how to really push healing after ShB. To be good you're required to DPS, you can't really feel like you're done and are okay if you just heal. That's ok, no one can force you to try your best but again, don't be surprised or offended with people not liking this.