Why abandon labels? Labels help us define and expand upon things we knew or feel or what is already there. If we didn't have labels, we wouldn't have cultures, groups, communities or even knowledge on my anthropological things. We need labels so we can better understand ourselves.
To a point, yes. What you say has validity. However, the other side of that is that if you identify yourself as "X", you are less able to move beyond being "X" due to the desire to "be X". What happens is things like this, "I can't think like this, because an "atheist" shouldn't have feelings of God! What am I? A hypocrite? Not an atheist?". Apply that to a Christian who has doubts about God, "I'm supposed to be a Christian! How can I doubt God exists?". So while wanting to identify as something has its benefits, it also have its negatives. It keeps you within the boundaries of what the label defines that "X" as, and as a result of that, that group itself will stagnate and die by curtailing those who push against the boundaries of it, preventing it from evolving. Religions meet their death this way.
Now when it comes to the day and age we live in, this is very much more complex than simply wanting to fit into the culture at large! I believe there is a vastly far greater freedom afforded us through the rise of the Internet. You can find others who push the boundaries of doubt outside one's own group, including modern atheism for that matter. There is less compulsion to give up these "sinful" thoughts of doubt and question the 'norms' of that group where you are completely isolated without any sort of support at all, as would be the case in closed communities. Today, in larger modern societies, we can forgo religious communities in favor of larger "non-local" communities. We can hear of others working out their paths outside the mainstream, and get support from them by simply reading what they've worked out. Or actually participation with them directly in online forums, such as this one.
In this larger context, the label, becomes less defining in a lot of ways since you have "Christians" or "Muslims", or "Atheists", of all manner of diverse views, from uber fundamentalists within each group, to ultra liberals and progressives. In local groups, tolerance like that is a little harder to maintain unless you have truly good leadership at the top, where they can keep the "I've got the real truth!" elements from eating each other alive. It's easy to put someone on the "ignore" list here, plus forum rules are designed to not let the militants ruin it for everyone else, to prevent them from trying to convert everyone to their way of thinking.
But the other factor I did not touch on was this. Someone on their own path away from these throttling groups may find identifying by that label to hinder them in truly stepping beyond what was programmed into their minds by the group. The group claims to "own God", in all intents and purposes, and so in order to "save God" from them, one has to say "I'm not them!" first in order to find themselves. Then later, if they want to call themselves by that lineage, they can do so now being empowered to say they don't have to fit their notion of what "X" is nor believe they "own God" or "truth" as they had been taught previously by them.