Hi Joseph,
Sorry to hear about your problems with that Mobo. As Saltgrass indicated you might have a down-rev board, or just a bad one.

Specs here on your Model number do show it to come with UEFI BIOS standard. Not having that option is certain rare--I've never seen one either. We are aware of some UEFI's without the legacy or secure-boot settings however from other users and techs here on our forum. Here's the link to the spec I looked up on your Board:
ASUS P8H67-M EVO (REV 3.0) LGA 1155 Intel H67 HDMI SATA 6Gb/s USB 3.0 Micro ATX Intel Motherboard with UEFI BIOS - Newegg.com
I also noticed that out of 45 reviews on this Board, on the newegg site; it only scored a
27% out of 100% rating. That's extremely poor for any Mobo let alone ASUS,

which I consider to be the top of the line in Mobo manufacturers. As that Board is 3-5 years old, it was just probably a very badly designed board, and should have been replaced as soon as you uncovered that problem. But unless you did a Multi-OS boot as Mike and others mentioned or you boot from diagnostic media such as DVD disc or USB stick you would never run into it during normal use.
I would suggest you scrap that Mobo and buy a new one. MSI now has W10 certified Mobos with proper UEFI BIOS, and all of their Mobos I've seen have the secure-boot option in there. Here's a link with more information:
MSI First Motherboard Brand to be Windows 10 Certified
Since you have a self-built PC, you can just change it out. I would also look at your PSU specs when you do so, as a common precaution, as you may have to upgrade to a more powerful higher-wattage unit. You can downgrade your W10 if you don't want to upgrade the Mobo and run Win7x/8x, or replace it and do what I do with old Mobos here:
Best of luck,
<<<BIGBEARJEDI>>>