Your teacher is correct. Secondary cell walls make the cell walls more resistant to degradation, but are less flexible and decrease the amount of water permeability. Pits are openings (holes if you prefer) in the secondary wall that are used for cellular transportation. They are also responsible for allowing cell to cell communication by letting the plasmodesmata connect to other cells through the secondary wall.
So, if a plant cell has pits, it has a secondary cell wall, because pits are openings in this specific wall. As we will see, not all plant cells have secondary walls!
Secondary walls are only present in cells in which it develops. An example of a plant cell type without a secondary cell wall (thus without pits) is the parenchyma, one of the main types of plant tissue.
Lacking the secondary wall, parenchyma cells are known to be more flexible, as they are thinner.
I hope I gave you the proper definition you were looking for, and was able to give you a clear understanding of which plant cell types contain pits!