When you send a message by email, it must have, somewhere in the message, the addresses to which it is sent. Some mail clients are somewhat deceptive in that they show just display names, leading users to assume that the email addresses are somehow suppressed. Even if those same mail clients perform the same sleight of hand on receipt, a savvy user would be able to view headers or message source and discover the full addresses. Thunderbird is honest with you and shows you what is being included in the message.

If you want to send a message where the recipients cannot see each others' addresses, Bcc is the appropriate way to go about it. Click on "To:" and change it. Set it to Bcc before you add any addresses and they'll all be Bcc, because it copies the previous setting as you add each addressee. There are add-ons to make the switch to Bcc automatic.