Page thumbnails (used in search and in embeds) don't always pick the image that you would expect. Recently, I had issues with the main page of my wiki when its thumbnail insisted on not being the first image, which was the most fitting, and instead picking the largest image instead. I would like for the thumbnail picking to be more intuitive or for me to be able to manually choose the thumbnail.
This is due to the way that PageImages, an extension made by the Wikimedia Foundation who develops MediaWiki and owns Wikipedia, scores images. The criteria for how it scores images is on the page I linked. You can exclude an image from being considered by the algorithm by inserting class=notpageimage into the image tag of the image which is selected by the extension.