2016 tour:- India had Ashwin/Jadeja who are deadly at home but Cook got a hundred on the flattest pitch of that whole season( Aus/SA/NZ all toured but Rajkot was the flattest, even Moeen and Stokes got a hundred). He struggled against Jadeja as well and ended up with an average of 35 which was very mediocre <B>but</B> only England were served with those flat pitches in whole session.
2012 tour:- He delivered his career best performance by delivering three hundreds but bowlers were Naman Ojha and a newbie Ashwin who was bowling trash. Ojha was India's leading spinner at that time. His inning on rank-turner was a great one but KP completely overshadowed him by not just scoring but destroying Indian attack there.
Overall, he has done great against India and Australia but cashed on easier attacks. Even his 290 in Abu Dhabi came against the worst Pakistan attack I have ever witnessed.
Now, all this doesn't make Cook a bad player( he is a great test player) but stating that his average is low because he has played against top attacksand in toughest conditions and his average would be 55 if he batted at 4 is exaggeration of another level.