GTO Trainer... checking pair of aces on dry flop as PFR

Here's another hand I could use clarity on.     I am in MP2 with AJo and the Button calls.  On a Flop of A72r, i bet 1/3 pot, but Trainer preferred I check.  On the Q turn, I bet 2/3 pot, but Trainer still preferred a check.   When the Ten came on the river, I checked, but Trainer recommended betting (92% of the time).

Could you please provide color on why checking the flop and turn and betting the river are the desired actions in this hand?

Thank you!

J