I would say there is something wrong with apples product if it does not delete them when your do and you have a setting of leave messages on the server until I delete them. But I am unsure if it even has such an option, from what I see it is remove when you download of after a time.

To quote you.

The emails in my Yahoo Webmail are being moved to the trash whenever I delete my emails in Thunderbird even though I have the "Leave messages on server until I delete them" box checked.

You deleted them. so they are being deleted on the server. What part of that statement would not be self explanatory? The setting says leave until you delete and you deleted.

Perhaps you need to uncheck the "until I delete them" and leave it just as "leave message on the server." that is what you sound like you wanting.

Thanks Matt, you are correct.