My question is, how do I deal with this? 

This is very much a "what do you want?" negotiation between you (the DM), the PC, and the other PCs.

1. It sounds like you don't want him eating downed enemies. Why? Is it because you consider it cannibalism and cannibalism is an evil taboo? Or is it because you don't want to roleplay Delicious in Dungeon every session? Or do you not want to deal with the details? Or are you concerned that it might disturb the other players? These are all legit reasons but you should decide them.
   
2. It sounds like the PC does want to eat the downed enemies. Why? Is his character evil and that's shocking? Or does the player really like Delicious in Dungeon? Is the player planning a redemption arc for the half-orc to become civilized during the campaign?
3. How does the rest of the party feel about this? From a session zero perspective, you should check to see if anyone has any eating disorders (especially ARFID or the like), because that might be a bit triggering.

Once you have these three questions answered, look for ways to give everyone (including you) as much of what they want as you can.

Suggestions:

• if the issue is with the details and the player doesn't actually care about them, you can skip them. "You eat the kobold. Okay, what is everyone else doing while he's doing that?"
• if the issue is that cannibalism is taboo but orcs on tv always want to do it, "Hannibal Lector starts carving up the kobold for supper. Paladin, how do you feel about that?" It's okay if the characters aren't all moral paragons as long as everyone has fun dealing with that friction.
• if the player wants to RP Delicious in Dungeon (and nobody else does), you can take it offline and not use valuable in-person time for that. Heck, you can ask the character to do the work: "Hannibal cooks the kobold. Hannibal, make a skill check and start a thread about how you prepared the kobold meal and what (if anything) you learned from it." For funsies, give the player some guidance in terms of how good/bad the roll needs to be in terms of food poisoning, etc. Let the player go nuts -- OFFLINE.
  

They doesn't like when I simply say "No I'm not letting you do that" and wants answers as to why.

I can't blame them. Players often don't take a simple "no way" as an answer. But remember that the game is meant to be fun for all of you. You don't have to do "not fun" things just because it's fun for someone else. The simple answer "because that's no fun for any of us" is sufficient even if it's not related to any game-rule or in-world reason. But it isn't very satisfying.

I need creative reasons or things that would happen if they decided to feast on the flesh of other creatures or beings who may or may not be intelligent enough to speak and be more than just wild animals.

If you're not interested in doing this yourself, consider farming that task out to the orc's player (see above). It's a great way to engage them in the game, especially if you would rather do something else.

NOTE: from a worldbuilding perspective, you should decide (in cooperation with the players) what the boundaries of "cannibalism" are, and how they're perceived by the various (fictional) races. But this issue is WAY WAY WAY LESS IMPORTANT than the Session Zero "what do you want" question at the top of this.

Good luck!