I tried sharing your first post and the thumbnail is looking OK to me:

This isn’t really a theme-specific issue. If you’d like more control over what image is served up to Facebook you might want to look at the og:image management built into Yoast’s SEO plugin, which I see you’re already using. Here’s his guide on how to set it up:
https://yoast.com/social-media-optimization-with-wordpress-seo-by-yoast/
Hi Kathryn,
I don’t want the link to be displayed in that way, it is not appealing at all. I tried to share some blog posts belonging to other sites using your theme, and I noticed all of them have the thumbnail I’d like to obtain.
Go to http://theme.wordpress.com/themes/untitled/, and take for example roselinde’s and ychi’s sites (below, blogs using Untitled).
This is what I’d like to have when sharing.
Please tell me if you need more information to understand my issue.
Thanks!
I would like to add for me it’s important to solve this issue at least for Google Plus, don’t care about Facebook.
Thanks!
take for example roselinde’s and ychi’s sites (below, blogs using Untitled).
This is what I’d like to have when sharing.
Those sites are running on the hosted WordPress.com platform, where the underlying WordPress.com service outputs code that suggests sharing thumbnails and other meta data for social media services.
Since your site is self-hosted on your own hosting, I suggest you have a look at the Yoast settings for social-media. As I mentioned before, this isn’t something that’s controlled in the theme itself.