Note the following exchange between Firenze and Bane.
"My name is Firenze," he added, as he lowered himself on to his front legs so that Harry could clamber on to his back.
There was suddenly a sound of more galloping from the other side of the clearing. Ronan and Bane came bursting through the trees, their flanks heaving and sweaty.
"Firenze!" Bane thundered. "What are you doing? You have a human on your back! Have you no shame? Are you a common mule?"
"Do you realise who this is?" said Firenze. "This is the Potter boy. The quicker he leaves this Forest, the better."
"What have you been telling him?" growled Bane. "Remember, Firenze, we are sworn not to set ourselves against the heavens. Have we not read what is to come in the movements of the planets?"
Ronan pawed the ground nervously.
"I'm sure Firenze thought he was acting for the best," he said, in his gloomy voice.
Bane kicked his back legs in anger.
"For the best! What is that to do with us? Centaurs are concerned with what has been foretold! It is not our business to run around like donkeys after stray humans in our Forest!"
Firenze suddenly reared on to his hind legs in anger, so that Harry had to grab his shoulders to stay on.
"Do you not see that unicorn?" Firenze bellowed at Bane. "Do you not understand why it was killed? Or have the planets not let you in on that secret? I set myself against what is lurking in this Forest, Bane, yes, with humans alongside me if I must."
(Philosopher's Stone, Chapter 15, The Forbidden Forest).
I'm trying to decipher what exactly was the mystery in the heavens which Bane was worried Harry might have discovered. It seems to concern Voldemort, based on Firenze's final remarks. It seems to concern Harry somehow, based on how Firenze points Harry out, and on Bane's reaction to that.
When he comes to teach at Hogwarts Firenze says that he has read the breakout of a wizarding war in the stars.
"In the past decade, the indications have been that wizardkind is living through nothing more than a brief calm between two wars. Mars, bringer of battle, shines brightly above us, suggesting that the fight must soon break out again."
(Order of the Phoenix, Chapter 27, The Centaur and the Sneak).
The divination referred to in The Philosopher's Stone appears to be more specific, however.
Could it be that
Firenze and Bane foresaw the death of Harry at the hand of Voldemort in their Forest at the end of Deathly Hallows?
That would explain Firenze's desire to protect Harry. It would also explain Bane's reluctance to get involved in the affairs of humans if he believes that resistance to Voldemort is futile.
What did the centaurs read in the stars?