Some of the replies. 
OP you are not alone, sadly in my work place, people 'forget' their manners and attempt to enter a lift before letting people out. If you were to question politely, the rationale as to why the person was rude; they would likely bleat that it was a mistake and apologise. Outside work, people will be less compliant as there is no consequences and can say what they will.
My own reasoning, just observe the same ignorance which is prevalent when boarding public transport in rush hour. It gets carried over.
Slight digression, the Internet is the same - People hide as they are 'anonymous' and some are toxic because they can hide (rant over).

OP you are not alone, sadly in my work place, people 'forget' their manners and attempt to enter a lift before letting people out. If you were to question politely, the rationale as to why the person was rude; they would likely bleat that it was a mistake and apologise. Outside work, people will be less compliant as there is no consequences and can say what they will.
My own reasoning, just observe the same ignorance which is prevalent when boarding public transport in rush hour. It gets carried over.
Slight digression, the Internet is the same - People hide as they are 'anonymous' and some are toxic because they can hide (rant over).