You could lose your rank for keywords you are already ranking for. Whether you've put much effort into SEO already or not, most websites generate a good portion of their traffic from their organic search listings. Don't screw it up.
You could be rewriting content for no strategic reason. If you have an existing website, chances are that you're *almost* ranking for at least a handful of relevant keywords. When you're rewriting content, you should find out what those keywords are and then use them to guide your content creation.
You could lose the value of your inbound links. Existing links from other sites usually point to different pages on your site. They drive direct traffic and support your SEO. Make sure you map and redirect old pages to new ones.
You could do a lot of things that need to be redone again. SEO affects how you organize the pages on your site, your navigation, the words you use to name your pages and many more things that are more expensive and time consuming to change after you build your site.
So, if you're a marketing manager or a business owner relaunching your website, it's important for you to understand this process. Since this process requires thorough keyword research and since keyword research requires knowledge of the business, this should be a very collaborative process.
The company you hire should have these skills and collaborate with you, or you should find someone that will.