What does the word "on" mean in this context? (very difficult question)?

It doesn't really seem to be "due to" or "because of." Are there any other choices on your list that you have ruled out? It could be something like "from" or "to" or something like that. If you have to choose "due to" or "because of" (odd choices, as they are nearly synonymous) I'd say go with "because of."