Why do you need to turn off "Find my iPhone" for repairs?

It's so Apple can work on your phone without it having to request constant 'authentication' from one of your other Apple devices or iCloud.  As a computer tech, that gets very annoying having to ask the customer for their 'verification code' the moment changes are made.

For many repairs they will just swap your device out for a refurbished model. They will need all "cloud locks" (aka find my iPhone) to be disabled, so they can eventually repair and resell the one you turned in.   They will send broken devices to places like India or China in bulk and take months to repair them, which is why they need to do swaps to keep customers mostly happy. 

To prove you own that phone.

Also, it means if they have to replace it rather than repair it, the old one can be erased without any problem. That avoid them having any problems with security of your personal data.