I think this would be easier if we rank how important the electron interactions are in bonding: lone pair - lone pair (lp-lp) >> lone pair - bond pair (lp-bp), and bond pair-bond pair (bp-bp). The larger the separation between electrons the better, right?
Let's inspect your answer:
lp-lp interactions: 180o 
lp-bp interactions: 90o 
bp-bp interactions: 120o 
lp-lp interaction is good but you also have to consider the lp-bp interactions. There are 6 and most importantly they are 90o
For the correct answer:
lp-lp interactions: 120o
lp-bp interactions: 90o  + 120o 
bp-bp interactions: 90o 
Both structures would have large angle between lp-lp. So the decision is between lp-bp and bp-bp. Looking at the number of lp-bp interactions at 90o for your answer and the correct answer, the latter would have less 90o interactions than your answer. Less repulsions and therefore, much preferred.