I admit that one of the biggest philosophical questions in the workplace is something I struggle with - do you focus on your strengths or weaknesses when it comes to development?
As with most things, I don't think it is an either/or situation - there is some middle ground. I just don't know where that line should be.
One thing I do know for sure is that everyone - managers especially - need to be aware of weaknesses and accept them. Whether you work on eliminating the weakness isn't the point. Being aware of it let's you make the decision on how to address it.
For example, I am very comfortable with words, not so much with visuals or graphics. I also know that visuals and graphics are very important to communication. To be the best professional I can be, I have to consider visuals. Only through accepting this, can I make plans to address the issue.
I am actually doing several different things. First, for key things I hire a graphics designer. She does amazing work and has skills I can't replicate. I love the work she does and use her when I can. Second, I am trying to learn more about visual design. Color schemes, placement, tools, etc. When I can't use my designer, I have some knowledge that I can use to put something together. Third, I ask for more feedback. When I design something visual, I show it to as many people as possible. The additional feedback helps me see things my untrained eye misses.
The key is that I know the weakness, I know it is something that has to be addressed, and I have a plan for how to address it. None of that is possible if I don't accept my weakness.
What does not accepting a weakness look like? Diminishing something (visuals aren't that important - it is something that people who are too lazy to read want), ignoring weak skills (I'm not a designer, but I think it looks just fine), and a lack of creativity (basically copying other designs when you can find one that works).