What is the minimum wiring for two switches?

One can only guess to answer that question, as you don't tell us who has told you to do so.
One reason was already given:
If you or someone else has trouble with the fact that a non pressed button will result in a HIGH and a pressed button will result in a LOW, this is a hardware way to solve that.
Ofcourse you'd have to consider cost of the resistor (a few cents to buy it, some more to integrate it in your design and (relatively) a lot more space on your board) to that of programming in such way that you (so you, the Arduino doesn't give a rats *ss) will keep track of the status of that button / switch.