The short answer: Yes! That said, the real answer is a little more involved. At the end of the day, you want people coming to your website rather than other people's websites. But without putting articles on other people's sites, you won't get the exposure you need to build your own audience.
How much content should you put on your own site? How much should go on other people's sites? Let's explore these questions.
Why Put Content on Your Own Site?
There are many reasons to put content on your own site rather than someone else's.
First of all, search engines rank the site that has the actual content. If all your content is on someone else's website, that means they're getting the benefit of search engine rankings instead of you.
Secondly, people mentally give credit to the site they see content on. In other words, if they go to someone else's site and see your content on it, they give a lot of credit to that site. If that content was on your site, you'd get the credit instead.
In the long run, you want to be building your own personal brand and your own audience. You need to consistently put out great content on your site in order to do that.
How Much Content Should You Distribute?
On the other hand, putting content on other people's sites will get you backlinks as well as raw traffic. That can't be discounted, especially in the beginning stages of a new website.
An optimal mix is to start with about 40% of the content on your own site and 60% published on other sites. This will get you the initial surge of traffic and backlinks you need to start building your audience and getting rankings.
Once you have a few one-way links to your site and a few hundred people coming to your site consistently, then start building up your own site rather than other people's. Gradually cut back the amount of content you syndicate out and increase the amount of content you keep on your own site.
Once you're a well-known brand, you want to be publishing about 95% of your content on your own site rather than someone else's site. The other 5% will be strictly for guest blogging, for people you know, and for sites with strong reputations and traffic.
One quick point on duplicate content- Don't use the same content for your own sites as the content you syndicate out. Google will view this as duplicate content and dock your rankings as a result.
In answer to this article's title, the answer is "yes" - you should post your articles on your own site. In the beginning, you'll need to publish more on other people's sites to build traction. As your site grows, however, publish as much of the content on your own site as you can.