Cefey: This is from BALPA website, are they also wrong?
Despite what the schools will often tell you, there is not a shortage of pilots in the industry, nor are there signs of one occurring soon. There may, however, be a shortage of experienced pilots, those who have several thousand hours flying commercial jet aircraft. There is a stark difference between the two, and unfortunately most people who finish their flight training, even from the mainstream schools who claim to have good connections with airlines, often find themselves unable to even apply for the vast majority of jobs because they lack the experience required. This is something which the training schools will never admit to, but you will need to be prepared for.
Bridging the gap between qualifying and gaining employment is fraught with difficulties, and often requires buying expensive additional training in the hope of finding a job. You need to think very carefully before you enroll on a flight training course, and decide whether you can afford to finish the course and not find a job. Getting onto an airline sponsored scheme where a job is offered upon completion may be the safest way, but there will be fierce competition for places on such schemes.