Why would he do that when he can do what he did in fact do? He's got much more freedom and power to choose his career moves now, and Arsenal have much less (precisely: none). Can hardly blame him given the ridiculous choices we made with him (West Brom) and potentially with his fitness (shambles that our club was injury wise before the reform after 13-14). In every way not signing a contract with Arsenal, if he wasn't convinced he was going to be an important member of the squad as he should've been, was a better decision for his career.
When did I say that? I didn't.
People really have short memories. First of all it's logical he'd be a bit better 3 years older and more mature (his first couple starts were a bit nervy as to be expected, though the quality was obvious), but in his few starts that season he scored the winner against Swansea, won the winning penalty against Palace, produced a man of the match display against Spurs in the FA Cup, and had another fine display against Aston Villa. All these when we were very much in the thick of the title race (I repeat: at the age of 17). In the spring he was rightly preferred to Podolski before a few more players got fit and he got injured.