adb does not reboot my Samsung Galaxy SIII I9300 to bootloader (download) mode! My device is Samsung Galaxy S3 I9300 and I did a complete factory reset. Device is NOT rooted yet. It works properly. I can do all of following with my device:  


Power off using device keys.
Start in recovery mode and download mode using device keys.
device is detected properly in normal mode and recovery mode by adb when is connected to PC through USB cable
I am able to reboot device using adb reboot command
adb reboot recovery works well.


The problem is that if I run adb reboot bootloader or adb reboot-bootloader commands, device is booted in normal mode, NOT in download mode. The only way to reboot the device in download mode is to use Power + Volume Down + Home keys
From my experience with Samsung devices this is not a bug but rather a feature. The "download" AKA "ODIN" mode on Samsung devices is a proprietary alternative to bootloader/fastboot mode and I don't remember being able to boot to this mode in other than the hardware way.