Why do you think Kong and Godzilla will fight?

Well I think Godzilla will try to reach Skull Island get him to submit.

Yeah, that's part of my own working theory right now.

More specifically, I speculate that Godzilla wants to claim Skull Island in its entirety as part of his territory. Presumably, it's been independent as the territory of Kong's species and thus not counted as Godzilla's turf as the rest of the world is.

It could be that the incident with Ghidorah has gotten Godzilla to be a bit more proactive in managing his domain and claiming new territory as his own.

Yes, but I think another reason why Kong and Godzilla will fight is pretty much which each Titan represent in the Monsterverse. Godzilla is Restorer of Balance, Kong is the Protector of Mankind

That sounds interesting. I figured something like that would be the case. But I think that skull island is also an important territory to have because in the movie it has many hollow earth points. This could also be why Godzilla wants it. It’s the center of the titan world to put it simply. 

Probably something about territory/dominance.

The fight will be due to human manipulation. People will ultimately be responsible for the fight. It was stated in the KOTM credits that Monarch is doing something on Skull Island. Whatever they are up to will most likely spark a showdown between G and Kong.

Maybe because Godzilla has some past with Kong's species?

I don't have any other theory...

Maybe Monarch is doing something on skull island that causes G and Kong to fight...

Freaking MONARCH! What did you do?!

I can't wait until this movie comes out, Bombs and people will finally stop asking this stupid effing question. And I tell you this: If they retcon this universe and have Godzilla's species be responsible for the death of Kong's parents and not the skullcrawlers just for the sake of the plot, Then this universe deserves to die a nasty, horrible cinematic death. <Whispers>  it already is anyway. 

@MACUMBALOVE

They already established that Mamma Skullcrawler killed Kongs parents, so why in the hell would they retcon it to be Godzilla? Stop your hate of the monsterverse.

@macumbalove - you seem to take great glee out of the Monsterverse failing. Why are you here?

@macumbalove, well aren’t you a little ray of sunshine. If the monstersverse is so shitty why bother with this website. If I asked a stupid question, why bother giving it attention? Shut the hell up and waste your time on something you really care about than with this site.

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Really the only thing that needs to happen is to exploit what both Characters are about. Godzilla is an anti-hero who fights to keep nature in balance and will come to blows with anyone threatening that balance. Kong is a sympathetic creature who fights to protect the weak.

We see in Legendary Goji that he's been around for awhile. He's seen the dangers that the world has to offer, This includes the Humans.

Kong, Is still relatively young, his encounter with humans has mostly been a positive one despite a few bad apples, He's capable of figuring out which humans specifically are bad and which ones are harmless and he tends to give them all a chance to show their true colors before acting out at them.

We know Monarch has been on the island working on some new tech. The very threat of a new weapon should be enough to put them on Godzilla's radar. Especially if testing causes restlessness of the creatures on the island.

Kong, Having been around them for awhile now, doesn't see the harm in their presence as they tip toe around him. (Monarch would know better than to openly blast the island by now.) It may even be that a specific human or group of humans has befriended Kong.

This is really the only set up you need.

Godzilla shows up, sees what monarch is doing and begins to take them out. He's destructive and Kong doesn't like it.

Godzilla gets the upper hand with his experience on their first encounter but Kong survives. The Humans then employ their tech to help Kong in his next fight and Kong fairs much better the 2nd time around. Godzilla refuses to give in and pulls out all the stops. In the ensuing chaos The humans unleash their new weapon and it gets a few of Kongs friends "Be it Creature or Human or otherwise." killed and Kong realizes the dangers of the weapons the Humans possess. Just as Godzilla is about to atomic breath the Monarch base, humans and all. Kong steps in and destroys ONLY the tech in front of Godzilla. Leaving the humans alive but defenseless.

Seeing the humans are no longer a threat and with a look in the eyes of Kong saying, "I'll keep the humans in check you don't have to worry about them.", Calms Godzilla's rage and he leaves the island with a new found respect for Kong and a promise to be back should their be any more monkey business.

So you leave with the knowledge that while Godzilla is King of the Monsters, Kong is King of the Humans.

Ps:

Regarding their ancient rivalry, I'd play it out something like this.

Kong and Godzilla species are both Alpha Predators. But they usually take turns between reigns. So it's not often that one of the members species is roaming the surface at the same time as the others. But it has been known to happen in the past that when the two happen to be awake at the same time, they don't always get along. Despite both being protectors of life, They have opposing views what exactly that means.

Intersting question and I think Morphrelink gave a nice break down.

I see Godzilla about keeping balance. Kong does that too except he seems to focus more on humans.

Why would they fight? Maybe Godzilla just sees humans as a threat to balance while Kong sees humans as being worthy of being spared?