Why does rooting void warranty? What is the reasoning behind Samsung being against rooting?
Why does rooting cause your warranty to be voided?
Isn't rooting a good thing for the user, since you have added functionality?
I understand that there comes security risks with rooting, but I'm sure if Samsung gave their full support to users that want to root their phone by making it an option, that they could avoid/fix security problems that come with rooting
What is the reasoning behind Samsung being against rooting? Why does rooting cause your warranty to be voided?


It is not a Samsung-specific case. Almost all manufacturers demand you to use the device as is. It is mostly about risk management. The risk of user damaging the phone is increased significantly when the phone is rooted and it would create a very big burden on manufacturers both as work force and economically. When they manufacture a series, they do it hundreds of thousands in numbers. They expect a number of problems with certain percentage of phones manufactured. If rooting is allowed, it would add greater risk and make the number of expected faulty phones unpredictable. 


  Isn't rooting a good thing for the user, since you have added functionality? 


Yes, as long as the users know what they are doing, but you obviously fail to see how unrelated this fact is to the question you ask. All computers have their own security-usability ratio. The reason you need rooting in the first place is because Android deliberately restricts the access of the user to certain properties. Not many people cares about getting to set CPU frequencies of the phone but many people cares about having a phone that is malware-free.

When you use a phone as is, the odds of creating bootloops, hard-bricks, security problems, usage of unauthorized software etc. is minimal and that is the way warranty-providers want to keep it. And that is not even the whole story. Manufacturers get paid to install bloatware. They don't want you to be able to delete them that easily.


  I understand that there comes security risks with rooting, but I'm
  sure if Samsung gave their full support to users that want to root
  their phone by making it an option, that they could avoid/fix security
  problems that come with rooting.


You are sure but you are wrong. You don't understand the root user concept of Unix-like operating systems. It is risky, period. You are free to use your device the way you want but you can't ask manufacturer to cover the expenses you might create by using the phone the way you are not told to do.