: Why do jazz theorists see church modes as scales when chant theorists (who use the older system) do not? Many jazz theorists say that we have seven (church) modes. The first one, they say, is Ionian. The second, they say,

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Jazz theorists don't use the church modes; they use the diatonic modes, which happen to share names with the church modes -- themselves named after the ancient Greek modes.

For a general explanation of the three sets of modes, see here.
For information on the diatonic modes, see here.
For the church (Gregorian) modes, see here.
And for the Greek modes, see here.

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Modern modes (Ionian, Dorian, Phrygian, Lydian, Mixolydian, Aeolian and Locrian) are simply scales using the major scale notes, but rooted in different places. Players using them prefer the changed flavour they bring. Lydian gives the sharpened fourth when compared with the standard major (or Ionian).
Anything which is presented in a rising and falling order in music is called a scale, it's just that Gregorian chant wasn't regarded as a scale, even though that's what the ordered notes were. At the time, the Ionian mode wasn't so important as it is now. So it is seen as the first mode, if you like, making the mode on its second note Dorian.
Originally,, Dorian and Hypodorian were extensions of each other, thus called 1 and 2. That meant there had to be 12 altogether, but there were never 12 roots or tonics. Only the 7 that we still use. Locrian (still relatively unused) didn't feature, so that's where the double 6 making 12 came from.