I used to do the lab. work for a local group of oncologists, and one evening I heard someone crying in the waiting room. The rest of the staff had left and the doctors were doing rounds, so I went to see what was going on. I found a patient sitting there, crying quietly. She had been in remission twice, but had recently relapsed. She said she needed to talk to one of the doctors because she didn't know what she was doing wrong. When we talked further, she said she had been using some visualization tapes, where you are directed to imagine that lasers or your vigilante white cells are killing your tumor. She had also been using some "positive thinking for cancer patients" tapes where you are told to repeat, "I am healthy" and "I am cancer-free." She was incredibly upset, not so much by the cancer, but because she felt that her inability to cure herself with positive thinking meant that she was doing something wrong and it was her fault. For me, that moment confirmed that positive thinking, used in the wrong circumstances and for the wrong reasons, can do more harm than good. The Antidote explores that interesting idea.
Oliver Burkeman is not out to bash positive thinking, but rather to explore "the negative path", the idea that the more we search for happiness and security, the less we achieve them. This is done through chapters on Stoicism, the ways goals can be counterproductive or destructive, insecurity, the non-attachment of Zen Buddhism, failure, and our fear of death. He presents ideas about what might make our lives less unhappy, but this isn't in the typical self-help form of strict rules or a program to be blindly followed.
The conclusions Burkeman seems to come to are to embrace insecurity, and stop searching for happiness and quick fixes. Rather than thinking about everything in a positive way, it is much better to see things realistically, accurately, and truthfully. That is a philosophy I wholeheartedly agree with.