Answering ‘why’ questions in evolutionary biology (and biology as a whole) is extremely difficult. Who knows? is the honest answer for the vast majority of questions; speculation - informed speculation - is often the best we can do.
Typically, chromosomal or genetic sex determination (GSD) results in a ~1:1 ratio of male to female offspring. This can be advantageous when the temperature of incubation does not differentially influence the fitness of sexes; that is to say, if males and females are both equally aided or abetted by temperature differences during incubation.
However, where temperature has differential influence on the fitness of individuals of different sexes, an environmental sex determination (ESD) system should be evolutionarily favourable; if males have superior fitness to females at low temperature, then selection will favour males over females at these temperatures, and it is easy to imagine the evolutionary potential of that relationship. This mechanism is called the ‘Charnov-Bull’ model.
The dynamics of the Charnov-Bull model might differ between lineages; for instance in some cases, hot and cold temperatures might favour one sex, while intermediate temperatures favour the other; a parabolic relationship between sex and temperature might then exist[2,3].
The Charnov-Bull model was empirically shown to be true of Amphibolurus muricatus, a short-lived agamid lizard, by Warner and Shine in 2008. In their experiment, they exposed eggs to different temperatures, while manipulating the sex of the lizards directly by hormone injection, and were thus able to demonstrate differential fitness effects on sexes at different temperatures.
It has been suggested that reptiles are particularly prone to transitioning from GSD to ESD, because their incubation environment is so variable[4,5], which might explain the prevalence of ESD in reptiles, relative to other vertebrates.
Differential fitness of sexes is not the only evolutionary explanation for the prevalence of ESD; a further three have been proposed: (1) ESD is ancestral and selectively almost neutral, and is thus perpetuated; (2) ESD promotes group fitness by permitting adaptive control of sex ratio; and (3) ESD permits inbreeding avoidance by producing single-sex clutches. These, however, have little empirical support, and are probably less important than Charnov-Bull dynamics.
A whole lot more research is needed in this field, because the real answer to your second question is no, not really. Nobody really knows, but a lot of people are speculating. And that is intriguing. Novel approaches provide great potential for future research, and perhaps we may be able to answer the why and and the hows. But for now, real answers just don’t exist.
Charnov, E.L. & J. Bull (1977) When is sex environmentally determined? Nature, 266(5605):828-830 [Read here]
Warner, D.A. & R. Shine (2008) The adaptive significance of temperature-dependent sex determination in a reptile. Nature, 451:566-569
Janzen, F.J. & P.C. Philips (2006) Exploring the evolution of environmental sex determination, especially in reptiles. Journal of Evolutionary Biology, 19:1775-1784
Georges, A., T. Ezaz, A.E. Quinn & S.D. Sarre (2010) Are reptiles predisposed to temperature-dependent sex determination? Sexual Development, 4:7-15 [Read here]
Sarre, S.D., T. Ezaz & A. Georges (2011) Transitions between sex-determining systems in reptiles and amphibians. Annual Review of Genomics and Human Genetics, 12_391-406