There is not much point in asking a children so young why they are behaving in a certain fashion. They are very self-centered and pleasure-seeking at this age, with no introspective ability. So, when a young child is angry or upset, it is generally due to one (or more) of four factors: tiredness, hunger, illness or (and this is the most frequent) their pleasures are being interrupted. This is what your wife is experiencing at the pre-school. Straightforward behavior management might help a bit. To start, if your wife's arrival is always consistent (re: time), the teacher can remind your son ahead of time that his mother will soon come and she/he can then prepare him to be ready. Second, you can establish a simple reward system: if he's able to leave in a cooperative fashion, a treat (modest) of some sort (e.g., small lollipop) awaits him in the car. A 'star chart' at the school or at home, noting his successful departures, can enhance the power of such a system. Third, if he does have a tantrum, he can be put in time out at home for five minutes (sitting quietly in a chair; use a portable digital cooking timer to track the time).
The parents all arrive at the same time, and the teachers do try to prepare the children for their arrival--but the reward for good departure behavior is a good idea. It does appear that he does this more when there is a disruption to his usual school routine, ie they did not go out for recess because it was too snowy, for example, so I suspect he just feels like he is getting gypped by having to go home without doing everything he wants to. But it is very difficult dealing with these public (amid many clucking mothers) outbursts, especially since he is not one to frequently have tantrums.