why the family believe they must get rid of Gregor?

The family comes to believe that Gregor want to tazke over the house for himself, and that he wants to ruin the lives of his family. They have finally come to seeing him as nothing more than an insect and no longer see him as human. 

“He must go,” cried Gregor’s sister, “that’s the only solution, Father. You must just try to get rid of the idea that this is Gregor. The fact that we’ve believed it for so long is the root of all our trouble.”