Live wire and neutral wire should never come in contact otherwise there will be a short circuit... but when we take a two pin plug and insert it into the socket then at that time we don't see whether the live wire and neutral wire go into the right socket hole... we just insert... but if live wire and neutral wire of the plug come in contact with the neutral wire and live wire respectively of the socket then there should be a short circuit but there is not. Why?
First, many two pin plugs have one pin wider than the other (check out a few plugs). This is done whenever there is a danger of the sort of short circuit you are describing. The pins will only fit in one way.
However, most of the time current can flow either way through the device being plugged in and there is resistance between the two pins. For example, consider a light bulb. The filament serves as resistance between the two pins and it can be plugged in either way.