Hi,
Michael:
because the pullup current ( IOH ) on these parts is rather low and is not normally able to bias an NPN bipolar transistor fully ON

...using bad engineering it is possible to use additional external pull-up resistor between port pin and +5V. Let say, 2K2 or something such. The bad thing is that at switch OFF state (write 0 to output pin) it produces input current into MCU. But it is just an example how it may be done with weak current from pin Maybe does that teacher mean such way?.

during that time the relay coil will be ON. For some designs this initial click of the relay can be detrimental to the product operation or at least annoying.

Okay, from other side, it may be useful if the product is designed to have relay switched ON from power-on for a short time and then OFF for rest of time. Here we have such scheme used with one of projects.

Regards,
Oleg