That's a false dichotomy, though. You can be
part of a group and not succumb to toxic groupthink.
In many ways, groupthink can be enormously useful. In a sense, universities, books, and other knowledge dissemenation mediums exist to solidify useful groupthink. Maybe one guy comes up with some small piece of math, another guy on the other side of the world comes up with another piece, and everyone makes their various contributions until someone comes along and rolls it together into theory that advances the world.
People who don't think like the group are reformed or weeded out so everyone understands how to "properly" study the world and you don't end up with a bunch of cranks coming up with intellectually lazy speculations.
So that's good groupthink (but people don't call it groupthink, because groupthink is generally considered to be the negative version of that). The problem is when groupthink becomes detached from reality.
But back to your original point: no, if I'm part of a larger group and I start to disagree with them because I think they are wrong, that does not make me part of a group. It's just me. I could organize a group of dissenters and form a critical mass to change the group, but that's not typically what I do.
Furthermore, the argument that "everyone is unique like you" to criticize counter-cultural movements is attacking a strawman. Maybe unintelligent teenagers think they're radically unique. But counter-cultural movements are very much groups. Humans work best in groups. We think best in groups. No one can accomplish very much alone.
All the thoughts I have, and all the thoughts you have, are plucked from the ether of the prevailing beliefs of our times. I can explain to you my personal philosophy, and you could sit down and trace my intellectual lineage if you really wanted to. You could observe how I picked the belief I'm arguing for after reading Carl Sagan at 16. He got it reading some other guy who got it from Schopenhauer or something. Maybe some of my Baptist upbringing is sprinkled in too, which comes from the Bible, in a line of intellectual descent that can be traced back to Zoroastrianism and beyond.
In the meantime, there are a thousand other youngish programmer dudes who read the same books that I did, and we talk to each other on the internet and reach group consensus. We bounce ideas off of each other and bring each other in line -- just as we're doing to each other at this very moment, on this very forum.
People who think they're radically unique are wrong. We're social animals. But that doesn't mean having the courage to dissent isn't important.