A few years ago, syndicating your blog was a way to distribute your online content. You could reach more people, and get more links to your website. Many internet marketing companies recommended this practice, and proudly showed "spikes" in web traffic for blog posts. However, syndication has sunk in favor, to the point that Google will punish you for doing it incorrectly. The "benefits" of syndication are nearly null, and ultimately only hurts your website.
First, syndication may reach more users, but those users aren't potential clients. Getting more readers to your blog seems great, but if those readers don't live in your city or state, why bother? You should want readers who could be clients. While syndication gets you more traffic, that traffic doesn't matter to your bottom line. Instead, focus your content on serving the needs of your potential clients.
Second, syndication for link building can HURT your website's search ranking. Google is punishing some forms of syndication because it creates false links. When you syndicate your blog, you are getting links back from many sources. At first this seems good, but if you are getting linked to by a website that publishes "spammy" content, it will do more harm than good. Google puts a priority on websites that have a good online reputation, and punishes those who are known for bad content and links.
Third, link carefully. Webmasters often get emails from organizations asking for a mention in a blog post or article. If the company asking is someone you know and trust, and the content is relevant to you readers, then linking to another website is okay. However, link sharing is a violation of Google's policies. If you choose to link to someone, do it without expecting a link in return. If you receive a "if you link to us, we'll link to you" proposition, ignore it.
Syndication seems like a good idea, but generally all it does is send your content to poor websites to be published. You should want your content shared by websites with great reputations, and if you are syndicating content, you don't know where it is going. Sending your content out on the internet blindly does not benefit you at all.