First off, you probably agree that publishing poorly edited copy (or copy that hasn't been edited at all) reflects extremely badly on the organisation responsible. How many times have you seen a mistake in the newspaper, an ad, an annual report, a sales letter or on the back of a bus (“How's my diving?”)?
Secondly, you probably also agree that your clients and customers should feel a) that they're getting value for money and b) that you know exactly what you're doing - otherwise you wouldn't be writing stuff and you certainly wouldn't be taking the time to check it. You'd be having a cappuccino instead.
But the unfortunate reality is that your closeness to your writing tends to blind you to its flaws - and sometimes, to autocorrect it. The UK-based Society for Editors and Proofreaders explains the phenomenon: “You hold the whole text in your mind, and you've developed its ideas in sequence right to its conclusion. You can't now put yourself in the reader's place by somehow ‘unknowing' any of this.”
In short, you know what you meant to write, so your eyes just fill in the gaps, miss the typos, etc. No matter how many times you check it, your brain interprets what it wants or expects to read, not what is actually there. So while you may have all of the skills to deal with the editorial functions, you lack the cold, fresh eye that a copy editor can bring to your work, and this is what leads to mistakes creeping in.
A copy editor is also sufficiently detached from the writing process to spot the mistakes and inconsistencies that distract the reader. After all, when we're too close to things, we don't see them clearly - which can be interesting in our personal lives but is hazardous for the editing process.
As an alternative, you may not have the relevant editorial skills. This isn't a failure on your part - it's not your job to be able to clarify meaning; eliminate unnecessary jargon; polish language by editing for grammar, usage, spelling, punctuation and other mechanics of style; or check for consistency of internal structure. But there are wonderful nerds out there who do this for a living, and do it well (which is useful in a world where it's unwise to rely on spelling/grammar checkers originating from the illiterate US.)
Outsource. Copy editors work on all kinds of projects, from corporate profiles to CVs, newsletters to websites, textbooks to brochures. Whether you're a large corporation, a small business, a government department, an NGO or an advertising agency, copy editors can help you enormously.
They can cut through the confusion to make your message clean, clear, correct, appealing and appropriate. They can help you to get it right the first time, and within budget. And above all, because your image is so important, they can help you to find the right tone and to choose the right words.