The reaction between anhydride and primary amine is by the Nucleophic addition-elimination mechanism (NOT by SN2).
First step: Nucleophilic addition step (Rate determining step):
The addition of amine to carbonyl center (at the most electrophilic carbonyl center and it should generate least sterically hindered intermediate) gives rise to a tetrahedral intermediate (4 groups bonded to the carbon center), which is influenced by steric hinderance. Therefore the attack of primary amine will prominently take place at -CH3 end carbonyl center which is more electrophilic and gives less sterically hindered intermediate.
Second step: Elimination step (fast step, not a rate determining):
The internal nucleophile (O- of earlier carbonyl) reverts back to generate the carbonyl center and propionate ion is eliminated.
Note: As the mechanism of reaction is not by SN2, therefore leaving group stability is not the sole criteria.