Q: People have been telling me that I don't write well enough, and I am kind of insulted by it. I think I do OK, and don't really need to be better for the kind of work I do. How can I handle this?
A: Be grateful for the feedback, and start building your skills right away.
The inner game
First, settle down a bit. Take some deep breaths, and let go of any anger. It can be difficult to hear that you need to be better at something, but don't take it personally. In fact, it's generous of people to be that invested in your success and to take the time to share their perspective.
Now, focus on your writing skills. What specific issues have been pointed out? Your course of action will depend on the need. For example, are your mechanics, such as punctuation, weak? It could be a matter of structure — whether you communicate your point clearly and directly. Or it could pertain to the salience of your content.
Consider your audiences. Most people in business are at least sending regular e-mails; you may also be preparing status reports or other project documents. Do you understand what your intended recipients need in each item you send?
Think about your career goals. Are you achieving the success you'd like in your current role? Do you hope to be promoted, perhaps moving into management? Communication skills, including writing, will be key.
Finally, if you're still resistant to the idea of improving your writing, ask yourself what that's about. Insecurity may be undermining your ability to grow and progress, so make the effort to think it through.
The outer game
Start by making a plan. If you don't know where to start, your first step is to explore the feedback you've received in more depth. With an open mind, go back to folks who have offered opinions to get more detail.