How liking and disliking mechanism is developed? Every one likes different things, places, people, colors, flowers etc. 
I am interested to know how this mechanism is developed in individuals. If we suppose that it is started from home. 

Then why siblings have different interests. 

If it is from society then living in same society still siblings have different interests. Like if two brothers are class fellows too and live in same people. still they will have different interests.
Considering the classical discussion of nature versus nurture, we can assume here that part of the causality is nature (genes, epigenetics) and part is nurture (environment, upbringing). We are all born with a whole bunch of instincts, probably hundreds. Not all these instincts are in effect at a given time, and a baby of course is not going to be displaying those instincts which are not important to its current circumstances, needs, and capabilities. As a child grows, he or she will learn how the world functions and what causes what. This person will slowly build associations between various desires (and urges) and those objects, actions, and places that satisfy said desires and urges. Because each person has different biological needs (different genes means slightly different nutritional needs, ideal temperature, physical needs, et cetera), each person, even if brought up in exactly the same environment, will build different associations with different stimuli and ideas over time. Through a long chain of trial and error with satisfying one's inner needs, each person will further differentiate in preferences.

Although I have no proof on the matter, I suspect that of the various specific (non-general) instincts a person can have, different people have different ones enabled and disabled. This would make perfect sense from an evolutionary perspective since you would not want everyone to react the same way to the world around them -- they might all go extinct at the same time if they all reacted disadvantageously to an occurrence that became common. Not everyone (probably nobody) is good at avoiding all kinds of danger and solving all kinds of problems. Plus, a society is far more productive if different people are good at different things, so there is strong selective pressure for a "rolling of the dice" on specific personality characteristics.