Repeating unit of poly lactic acid (PLA)
In fact, both pictures show the same polylactic acid, only different disconnection points have been chosen:



The red disconnection (or your picture 1) is preferred because you can immediately see that it is a polyester. 

Edit:

Your teacher is right in that, during the polymerization, the $\ce{-COOH}$ group loses $\ce {-OH}$ and the $\ce{-OH}$ group loses $\ce {-H}$ to form $\ce{H2O}$.
Therefore, your teacher prefers this arrangement:



If we draw it the other way, it are the wrong $\ce{-OH}$ and $\ce{-H}$ at the end of the chain, in the sense that it are not the ones that will give water:



However, note also that in either case, the part between brackets is not formed by identical fragments.
The atoms are indeed the same, but since not all are connected to the same atoms, they are not all chemically equivalent. There are different functional groups. 
There are acid, alcohol and ester groups; mainly ester of course. 
So in reality, we are writing $\ce{[...]_n}$, but those $n$ are not all the same and thus it is not correct.

If you want to depict the whole chain including the polymer chain and the ends that can continue polymerizing, the most correct way is to draw the end monomers explicitly.
At that point, you can place the brackets where you want, since the structures are absolutely equivalent.