You're own expertise comes to the fore
There are several reasons for this. Firstly, if all you do is send people to blog posts and articles written by other people, your followers won't really know what you're about. While they will appreciate the fact that you can point them in the direction of good content, they'll have greater respect for you if you can occasionally communicate useful concepts succinctly within the site itself.
Links can be boring, and risky
Also, I think many people get sick of clicking on links after a while. I know I do.
Then there's the risk that links to other sites constitute. Sure, if your followers already know and trust you they won't worry that the link you've included goes to a risky site or just some lead capture page. (That's why you should always check all links you are tweeting and retweeting first, so you know that they're not dodgy or spammy.)
But if someone hasn't seen you before they don't know how reliable you are in this regard and may not follow you as a result. So, if you tweet some self contained tips and insights it will show them that you are a genuine and knowledgeable person. They'll come to respect and trust you a bit more quickly. Then, having gotten to know you a little, they're more likely to follow you as well as click on the links you do include.
They can be collated for further use
The other advantage of tweeting link free tweets: You can collate them into lists on the same subject as you go. So then you'll have raw material for blog posts and articles down the track.
They are still very shareable
And while tweets with links tend to get more retweets, a well crafted offering that's entirely self-contained can get shared many times over. That's one reason so many tweeps send a constant stream of "wisdom quotes" by well known authors to their followers. People enjoy reading them and retweet them a lot. The person who tweeted builds their network more easily as a result.
Knowing how powerful these tweets can be, it's definitely worth creating your own general or niche-specific wisdom tweets, then. They'll stand out in the streams of your followers and be shared around quite a bit. They'll show your followers how thoughtful and insightful you can be, too, and help build you a strong reputation as an expert.