When you hit crunch time on a project, the stress increase has the wonderful effect of showcasing the individual contributions which aren't always apparent. Strengths and weaknesses are illuminated most when risk (and therefore stress) is highest.
You may have heard others talk about stress as a way to weed out those who can't cut it. To identify those people with weaknesses and therefore cull them. Increasing stress works both ways, you can spot both weaknesses and strengths this way. The difference between smart people and lazy people is what they do with this information.
Surely, you can remove people based on their weaknesses, but is that really the best way to get top performers? Not in my experience, and I'm not the only one. A whole slew of authors are writing about this balance between strength and weakness. For example, Now, Discover Your Strengths by Marcus Buckingham, or Teach With Your Strengths by Rosanne Liesveld , Jo Ann Miller , and Jennifer Robison.
Historically, the path to improvement has always been through building up your weak areas, not downplaying them (or better yet, avoiding them entirely!). We give people feedback on the areas they aren't performing, ostensibly so they'll get better.
When was the last time you got a review or feedback that focused on what you did well and only glossed over how you could improve? We have been obsessed with it, and therefore churn out contributors who try and be well-rounded or generic, living in constant fear their weaknesses will be exposed. Because of this close-mindedness, they are never able to pour themselves headlong into their strengths. Like a fly buzzing around, they are constantly distracted by their weaknesses, so they never put full force into their punches.
This is most definitely not how I give feedback. If I'm going to spend energy and time to think about and communicate my analysis of someone else, it is going to be practical. We will celebrate your accomplishments and spend time talking about how you can use the things you do well to really knock peoples socks off and be smashingly successful. Then maybe if you have really pissed someone off or are offensively negligent in some area, we'll mention how you can either avoid those situations, or how to minimize the damage when they happen. There is no sense trying to make a surgical scalpel into a hammer.
For my own performance, the same rules apply. Certainly I am critical of my failures and short-comings, but only as they distract from my ability to perform with my strengths to their maximum potential. Rather then dwell on not being a white guy with shiny, gleaming, perfect teeth, bushy hair, a perfect handshake and who looks at home in a suit, I play my geeky, straight-shooter, mushroom-like role to the hilt. And then I bring a white guy with full hair, a nice tie, and a firm handshake to the meeting. He talks his white-guy talk and does the secret handshakes so I can focus on the important details necessary for us to actually deliver.
When we try and force people into being generic and "well-rounded" we are really asking them to knock off their typically square edges so you can shove them into your round holes. I like my edges and try to respect the edges of others.
No one can do it all. Recognize what you can do really well and then avoid or compensate for the rest.