Some websites choose to embed Instagram images onto their pages, rather than uploading images directly.
This method can be used, but can also prevent the images from appearing in search engine results.
On a Google Webmaster Hangout from August 2019, Google’s John Mueller noted that if users choose to implement images using the Instagram embed code, then those images then carry a noindex meta tag.
They use a no index robots meta tag. And this meta tag tells us that you don’t want those images indexed together with the page itself… So essentially by switching from a direct embed of an image on your website to using Instagram embeds, you’re kind of telling us that you don’t want these images indexed for your website.
This signal to Google is essentially stating that you do not wish the images to be indexed alongside your page.
This is important to note, as if you wish for images on your page to appear in the image search results, then you would be advised to not use the Instagram image embed method on your site.