Kryonoglou
For Facebook you need Open Graph tags in your header. Are you using a sharing extension which adds these? There are a few extensions out there, but I stopped using one recently because it was causing errors. Anyway, you need something like this:
<!-- Let the Facebook og tags begin -->
<meta property="og:title" content="Facebook Open Graph META Tags"/>
<meta property="og:image" content="https://davidwalsh.name/wp-content/themes/klass/img/facebooklogo.png"/>
<meta property="og:site_name" content="David Walsh Blog"/>
<meta property="og:description" content="Facebook's Open Graph"/>
<!-- For Twitter you need the following -->
<meta name="twitter:card" content="summary">
<meta name="twitter:url" content="https://davidwalsh.name/twitter-cards">
<meta name="twitter:title" content="How to Create a Twitter Card">
<meta name="twitter:description" content="Twitter's new Twitter Cards API allows developers to add META tags to their website, and Twitter will build card content from links to a given site.">
<meta name="twitter:image" content="https://davidwalsh.name/wp-content/themes/punky/images/logo.png">
I believe there are other options (additional tags you can add) but this is just what I found doing a quick Google search.