I understand that people have argued that the Gravemind was waiting for Cortana's solution to the Flood to be revealed. But then the Gravemind doesn't kill Master Chief when he could have easily close up one of his bio-tunnels. Unless someone can answer this definitively, there is a huge issue with the lore.
The Gravemind still needs to stop The Ark if he wants his Flood to survive.
The Gravemind knows that the humans are not 'willing' to activate the Halo Array, but The Covenant is still convinced it will start their Great Journey. So its actually in The Graveminds best interest that the Chief runs free, especially because the Gravemind has no means to leave Installation 05 and reach The Ark at that time.
It's also very likely he knew about The Ark, considering he has control over the Monitor of Installation 05.
I know this isn't a long or elaborate answer, but it is a good point of view. The Gravemind has no real reason to kill the Chief, Humanity has no weapon that can destroy the Flood that is already so far spread as it is on Installation 05 and Humanity wants to stop the Halo's.
The enemy of my enemy is my friend.
The gravemind was on high charity, but I am as confused as you are why the gravemind simply didn’t kill master chief. I mean, we saw his tentacles can go very far and even kill Truth, but they can’t attack the chief? I believe this was simply a plot hole in the story and bungie at the time wanted to end this game with a bang. Halo has never been one for boss fights, so it would seem strange for them to randomly change it and decide to fight the gravemind in some kind of epic duo. Personally, I feel the gravemind could have easily pulled chief down at any time, and at the same time, the gravemind would have known the infection forms would survive the halo ring activation and this could all have been part of his plan in order to get cortana back to the unsc. In the end, I feel this won’t be answered, not even with the new halo coming out soon. The best we can ask for is maybe a reintroduction to the flood in halo 6 and the gravemind explaining his master plan in one of the dreaded slow motion gravemind talk scenes we all despised.