LVDS/differential driver source impedance matching
Your supervisor is wrong.  For the topology you've shown, the parallel termination resistor goes at the end of the run, furthest away from the driver.
If this is not done, the signal &quot;sees&quot; an open circuit at the end, and there is a 100% reflection from the open circuit back to the source.  This causes the classic ringing seen on improperly implemented interfaces.
In order for this reflection to not occur, the parallel termination resistor needs to match or be close to the characteristic impedance of the trace.
There are a number of questions here on SE that address this issue.