Why can't I boot from an external drive in Yosemite?

You've used the wrong method. Do this: Create a bootable installer for OS X Mavericks or Yosemite - Apple Support.

This has been the new method since Mavericks. If you don't want to do it this way, then try:

Make Your Own Mavericks, Mountain/Lion Installer

After downloading the installer you must first save the Install Mac OS X application. After the installer downloads DO NOT click on the Install button. Go to your Applications folder and make a copy of the installer. Move the copy into your Downloads folder. Now you can click on the Install button. You must do this because the installer deletes itself automatically when it finishes installing.

2. Get a USB flash drive that is at least 8 GBs. Prep this flash drive as follows:

1. Open Disk Utility in your Utilities folder.
2. After DU loads select your flash drive (this is the entry with the mfgr.'s ID and size) from the leftside list. Under the Volume Scheme heading set the number of partitions from the drop down menu to one. Set the format type to Mac OS Extended (Journaled.) Click on the Options button, set the partition scheme to GUID then click on the OK button. Click on the Partition button and wait until the process has completed.
3. Select the volume you just created (this is the sub-entry under the drive entry) from the left side list.
4. Click on the Erase tab in the DU main window.
5. Set the format type to Mac OS Extended (Journaled.) Click on the Options button, check the button for Zero Data and click on OK to return to the Erase window.
6. Click on the Erase button. The format process can take up to an hour depending upon the flash drive size.

Use DiskMaker X to put your installer clone onto the USB flash drive. Wait for the process to complete which will take quite some time.

It works with Mavericks, but I don't know if it has been updated for Yosemite.

I can certainly verify that you can indeed boot from an external drive using Yosemite. I do it all the time for the exact same reason as you. My USB 3 external drive is a SuperDuper clone of the boot drive. No issues so it’s strange that you would have this issue. Did you install Yosemite on this drive? If so how? Is the external drive properly formatted. Bootable drives must be formatted using the GUID Partition Table, not the Apple Partition Map (which is standard on some third party drives).

Ditto, but I only use FW externals, so can't vouch for USB 3.0 externals.

27" i7 iMac (Mid 2011) refurb, OS X Yo (10.10.2), Mavs, ML & SL, G4 450 MP w/10.5 & 9.2.2

Thanks for the feedback, but you marked the wrong poster as the solver.😉