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I think the biggest reason is that it may be difficult to control your function generator with an output of only 5 mV.  Some function generators have different output ranges that are switched, then a volume knob that lets you select from 0 to the maximum for the current range.  Even if it has a 100 mV range, you are still only asking for 5% of that.  It may be difficult to adjust the volume pot with any precision at that level.

I would attenuate even more than just by 3.  Make it so that the function generator puts out between 50% and 75% of its range.  That should allow for comfortable setting precision, without pot scratchiness getting in the way.

One drawback of your instructor's method is that the common mode signal will be even higher relative to the differential signal you are trying to measure.  For a differential amplifier, you want to test common mode and differential mode signals separately.  Seeing the result of just one composite signal doesn't tell you everything is working.  At least do one test with both inputs tied together and driven relative to ground.  Ideally you get no signal out.  You want to make sure the resulting signal is attenuated by the minimum common mode rejection the setup should provide.