"Snobbery" is an incantation We speak to get a seretonin boost in the presence of people or groups that cause our seretonin levels to drop. It is one of many tools that can be used to attack or diminish those who are seen to have higher status than Us.
You've got the causation backward here. Snobbery is a tool that people use to assert or maintain social status, or in the attempt to attain it, especially at the margins (if you are clearly enough high status, you don't need it though you may choose it). Like other tools of the type (e.g. etiquette rules) it's main purpose is to define in-group/out-group dynamics in a way that is difficult to counterfeit for one reas…
Few people use the word to describe themselves as snobs (except ironically), and it is also rarely used about someone in one's ingroup. Rather, it is a derogatory term we use against others (of higher status or in competing ingroups).
All social groups have signaling systems that allows members (or wannabe members) to display that they are members in good standing of the group. Due to their exclusive nature, these signals may cause distress in outsiders, and perhaps especially outsiders who would secretly like to belong to the group.
And this is my point, when someone uses the term "snobbery", it is often saying something unflattering about the person saying it.
Sometimes, of course, the term is used to refer to someone of equal or lower status. In such cases, the term tends to hold a somewhat different payload, ironically to assert dominance or superiority over that person, by indicating, as you do, that the "snob" behaves has he/she does to disguise his/her uncertainty about his/her status, maybe in a sophisticated way. For instance, someone from an "old money" familiy can use this kind of accusation against "new money" individuals that display their newfound wealth in a "distasteful" manner.
Personally, I hold the opinion that the labeling is probably worse than the snobbery itself, and at least as effective at reinforcing distance and distrust between groups. If I spend time with people 10x as wealthy and twice as educated, I'm not provoked by their social signals (unless they are offensive on purpose). Likewise, if I spend time with people in a third world country that live on a dollar a day, I appricate it when they treat me like a person, not just someone representing the West, even if I do sometimes (without thinking) behave in ways they may seen as snobbery from their perspective.