"I don't believe in kicking away ladders. By that, I mean the ladders by which I ascended as a young writer, small magazines that didn't pay anything, and that sort of thing"

George Woodcock is referring to the chances he had as a young author to get his work released in small magazines that didn't pay anything. He is saying that he doesn't think in taking away those same opportunities from other young writers. He thinks that it is important to offer the same chances to others that he had when he was starting. He is advocating for the importance of supplying a platform for young authors to get their work out there, even if it doesn't pay. He thinks that it is very important to give young writers the same chances he needed to get their work seen and to assist them establish their craft. He is motivating others to not kick away the ladders that helped him ascend as a young writer.