Why is the middle digit of North American telephone area codes always a 0 or a 1?

This is no longer the case.

"At first, area codes were all in the form N-Y-X, where N is any number 2-9, Y is 0 or 1, and X is any number 1-9 (if Y is 0) or any number 2-9 (if Y is 1)."
https://en.wikipedia.org/wiki/North_American_Numbering_Plan#History

"After the remaining valid area codes were used up by expansion, in 1995 the rapid increase in the need for more area codes (both splits and overlays) forced NANPA to allow the digits 2 through 8 to be used as a middle digit in new area code assignments, with 9 being reserved as a "last resort" for potential future expansion. At the same time, local exchanges were allowed to use 1 or 0 as a middle digit. The first area codes without a 1 or 0 as the middle digit were area code 334 in Alabama and area code 360 in Washington, which both began service on January 15, 1995."
https://en.wikipedia.org/wiki/North_American_Numbering_Plan#Expansion_of_area_codes

Here's a list of area codes currently in use:
http://www.bennetyee.org/ucsd-pages/area.html

O.K.

Why, untill January 15, 1995, was the middle digit of North American telephone area codes always a 0 or a 1?

It allowed the switching equipment to recognize the string of 3 numbers as an area code without help from a human switchboard operator. Trouble was, both area codes and exchanges were running out of numbers, so more flexibility was needed. It was a good plan and it worked well until sheer volume of telephone accounts overwhelmed it.

"At first, area codes were all in the form N-Y-X, where N is any number 2-9, Y is 0 or 1, and X is any number 1-9 (if Y is 0) or any number 2-9 (if Y is 1). The restriction on N saves 0 for calling the operator, and 1 for signaling a long-distance call. The restriction on the second digit, limiting it to 0 or 1, was designed to help telephone equipment recognize the difference between a three-digit "area code" (with 0 or 1 as the second digit) and the three-digit "exchange" prefix (which had avoided 0 or 1 for the second digit, because of restrictions in existing switching equipment). For example, when a caller dialed "202-555-1212", the switching equipment would recognize that "202" was an area code because of the middle 0, and route the call appropriately. If a caller were to dial 345-6789, the 4 would be recognized as a long-distance call within the area code and routed as such, without waiting to see or guessing at how many digits the caller meant to enter."
https://en.wikipedia.org/wiki/North_American_Numbering_Plan#History