Another reason to think that personality can't be changed a lot is the finding that there seems to be a reasonably strong genetic basis for personality, something which is suggested by, among other things, twin studies. But again you may ask: does this mean that personality is not malleable? In this case, too, the answer, I think, should be: probably not. Also when something is largely genetically based this does not mean it can't be changed (read this).
A third reason why the consensus has been (and, to be honest, probably still is) that personality is hardly changeable is that psychology has, for a long time, been dominated by a fixed mindset. For decades, the idea has been dominant that the adult brain is hardly malleable. The last few decades, however, have shown a pronounced shift in thinking about the brain. The brain actually is far more plastic than was thought and this plasticity remains throughout are lives. New connections between neurons are constantly formed. Damage in one area of the brain can often be partly or completely be compensated, if one practices hard, by other areas in the brain. New neurons are constantly 'born' in the brain. Et cetera. If the brain is actually so plastic and remains so plastic, the idea that personality is malleable suddenly does not sound so strange anymore.
There seem to be few reasons anymore to believe that behavior and behavioral tendencies (and what is personality more that relatively stable behavioral tendencies) can't be changed. But that changing personality is likely to be hard is easy to understand. Much behavior which we displays, we display without conscious thought or control. A brain structure below the cortex, the striatum (especially the upper part of it, the dorsal striatum) regulates our habitual behaviors. When behavior is often repeated we start doing it more and more automatically and it is more and more regulated by the striatum. Changing such routine behaviors is not easy. We can learn new habits but generally this can only be done through deliberate effort which is largely controlled by our prefrontal cortex. By practicing new behaviors repeatedly for a considerable time we can certainly build new routines in the striatum. There have been some studies which suggest that this is indeed the case. Previously I mentioned this study. Now there is a new study which suggests that personality can indeed be changed through deliberate interventions (driven by prefrontal cortex activity), in particular implementation intentions (also known as if-then planning; read this):
Hudson & Fraley (2015)
Abstract: Previous research has found that most people want to change their personality traits. But can people actually change their personalities just because they want to? To answer this question, we conducted 2, 16-week intensive longitudinal randomized experiments. Across both studies, people who expressed goals to increase with respect to any Big Five personality trait at Time 1 tended to experience actual increases in their self-reports of that trait—as well as trait-relevant daily behavior—over the subsequent 16 weeks. Furthermore, we tested 2 randomized interventions designed to help participants attain desired trait changes. Although 1 of the interventions was inefficacious, a second intervention that trained participants to generate implementation intentions catalyzed their ability to attain trait changes. We also tested several theoretical processes through which volitional changes might occur. These studies suggest that people may be able to change their self-reported personality traits through volitional means, and represent a first step toward understanding the processes that enable people to do so.