Why isn't the transaction log getting truncated when taking a full backup?
Being in the full recovery model means you want the option of restoring to any point in time. That means having a full set of transaction log backups after any database backup.

Imagine you have a db backup from midnight yesterday and log backups from 6, 12 and 18:00. Now you take another db backup. If the log is truncated, you can't restore to 11pm (which would require the previous db backup and all the log backups since).