Why did Cutter betray Angier and lead Borden to kill him Angier at the end of the movie? Angier's wife drowned, Borden's wife hanged, Fallon/Borden hanged. But Cutter had no motive to do any of this, unless he was in cahoots with Borden. But the movie had no indication of this.
My understanding was that Cutter start sympathizing with Borden for his loss of life. Cutter was intially with Angier only, however when he saw that Angier got one innocent man hanged and also took his daughter just for revenge. So he got disgusted. Also, he wanted to destroy that machine because it was not magic trick but real dangerous magic/science leading to killing one person (Angiers clone) every night.
Same is told in Wiki in this paragraph
Cutter learns that Caldlow has bought all of Angier's equipment, including the machine. He visits Lord Caldlow to plead for its destruction. He recognizes Angier, who had admitted earlier that he has always been Lord Caldlow (he had used the name Robert Angier to spare his family the embarrassment of his theatrical career). Cutter is disgusted with Angier for letting Borden hang and taking Borden's daughter.
Cutter just feels betrayed that Angier had gone to extreme lengths for his Transported Man trick which is not a trick at all but real science was involved where a clone of Angier gets killed every night. Cutter knows this since he has seen the old theater dump where the walls were lined with glass tanks of decomposed clones. Throughout the movie we have seen that cutter believed in a good magic trick but isn't very approving of Angier's obsession (even when he breaks the news of going to meet Tesla). Adding to this are the other facts that Angier framed an innocent Borden and took away his child from him. So Cutter had all good reasons to side with Borden even though he dint know about Fallon yet.
My comprehension of this is Cutter learned about the inhumane things which Angeir was doing- making clones of himself, and if you remember the scene where cutter says - "I once told you about a sailor, he told me drowning was like going home, I lied it was agony ". It clearly implies of all the murders Angeir was doing of his clones as every time new clone didn't know about the agony in drowning, it would have been considered Sacrifice if he had known the pain in dying but he was willingly killing himself. That's why Cutter helped Borden killing Angeir, In addition, separating daughter from father is also a considerable factor.