It's flattering when a website wants to repost your content via a syndicate arrangement. As an early website or blog, you may want to syndicate out your content in an attempt to increase exposure.
As a person with SEO awareness, I've never wanted to syndicate my content because I figured that if my blog had an article, I wanted to build links to it at my blog, thereby strengthening my link power for my blog as a whole, and that post in particular. If I posted my content on another blog or website, and people linked to it, then those links do not help my website. My name gets out there, but really, in the online world, you need to have a heavy hitter website or blog in order to have traffic and influence on the web.
That said. Someone in a forum shared a link with me on Google's approach to duplicate content and syndicated articles. It validated my gut instinct of not giving away content since you are essentially competing against yourself. From Google:
"Syndicate carefully: If you syndicate your content on other sites, Google will always show the version we think is most appropriate for users in each given search, which may or may not be the version you'd prefer. However, it is helpful to ensure that each site on which your content is syndicated includes a link back to your original article. You can also ask those who use your syndicated material to block the version on their sites with robots.txt."
If you are going to syndicate, you could and should seek out a link from the website who is reposting your article, and most likely, they will not want to block that content from being indexed because they are using your content to create more content on their own websites - without writing it themselves. Therefore, you could consider compromising by allowing them to publish an abstract of your article, with a link to your website or blog to get the rest of the article. Good luck!