Nah, you shouldn't be pulling if you're not the tank.
I definitely wouldn't recommend doing that, even if your tank is going slow. Newbie tanks especially need to learn at their own pace how much they can pull. It's frustrating when you're trying to manage aggro and someone else keeps pulling ahead of you - for the healer, too, since they now need to keep an eye on both the tank and the DPS who's pulling. Newbie healers can also struggle to heal tanks who pull big.
Yeah I know lol. I was the healer so that's why I did it. He did fine though. I don't the he noticed I was being a prick either.