Have you ever seen an old photo while sharing a web page? For example, when sharing the home page. This is because the first time you share it on Facebook, it will cache the photo. That's why you don't see the photo in your post the first time you share it. To clear the cache for the webpage you're sharing, go to the Facebook sharing tool:
Enter a webpage address in the field and click the "Debug" button. Then press the "Scrape Again" button. This will update the image for your post.
You should see the new photo. You can read more in the Facebook documentation.