You are correct, copyright remains with the person that took the picture, however by uploading it (and depending on your sharing settings) you grant a royalty free permission for Facebook to use the images however they like including for commercial gain So long as the image or any shared copy of it remains on their platform. So even if you delete an image if it has been shared publicly and is on someone else’s page they can still use it however they like.
“3. The permissions you give us
We need certain permissions from you to provide our services:
Permission to use content you create and share: You own the content you create and
share on Facebook and the other Facebook Products you use, and nothing in these
Terms takes away the rights you have to your own content. You are free to share your
content with anyone else, wherever you want. To provide our services, though, we need
you to give us some legal permissions to use that content.
Specifically, when you share, post, or upload content that is covered by intellectual
property rights (like photos or videos) on or in connection with our Products, you grant
us a non-exclusive, transferable, sub-licensable, royalty-free, and worldwide license to
host, use, distribute, modify, run, copy, publicly perform or display, translate, and create
derivative works of your content (consistent with your privacy and application settings).
This means, for example, that if you share a photo on Facebook, you give us permission
to store, copy, and share it with others (again, consistent with your settings) such as
service providers that support our service or other Facebook Products you use.
You can end this license any time by deleting your content or account. You should know
that, for technical reasons, content you delete may persist for a limited period of time in
backup copies (though it will not be visible to other users). In addition, content you delete
may continue to appear if you have shared it with others and they have not deleted it.”