A little more info for those who are curious: The perfect intervals (unison, 4th, 5th, 8ve) can be modified by being diminished or augmented, which shrinks or expands the interval by one half step. The other intervals (2nd, 3rd, 6th, 7th) can be either diminished, minor, major, or augmented. The major interval is what you'd get if you're measuring the intervals on a major (Ionian) scale; minor is -1 half step, dimished -2, augmented +1.
My intuition about which intervals are major / minor and which are diminished comes from the intervals that create the differences between the major and minor scales. The major scale uses all major intervals; natural minor uses minor 3rd, 6th and 7th; Dorian minor has a major 6th, and harmonic minor a major 7th. That still doesn't account for why the 2nd is called major / minor -- you could argue that you use it in Phrygian mode, but then you'd have to acknowledge that you use the diminished 5th in Locrian mode, so why not call that the major / minor 5th? (But almost no music is written in the Locrian mode).
Another intuition is that the fourth and fifth are the most consonant intervals (because the ratio of their frequencies is simplest) and so an adjustment of a half step is more of an increase in dissonance than a similar adjustment on another interval.
Finally, non-perfect 4th and 5th intervals are simply encountered much less frequently than other intervals (with the exception of the tritone between the 3rth and 7th of a dominant V chord, the characteristic dissonance that sets up the V-I authentic cadence).
My intuition about which intervals are major / minor and which are diminished comes from the intervals that create the differences between the major and minor scales. The major scale uses all major intervals; natural minor uses minor 3rd, 6th and 7th; Dorian minor has a major 6th, and harmonic minor a major 7th. That still doesn't account for why the 2nd is called major / minor -- you could argue that you use it in Phrygian mode, but then you'd have to acknowledge that you use the diminished 5th in Locrian mode, so why not call that the major / minor 5th? (But almost no music is written in the Locrian mode).
Another intuition is that the fourth and fifth are the most consonant intervals (because the ratio of their frequencies is simplest) and so an adjustment of a half step is more of an increase in dissonance than a similar adjustment on another interval.
Finally, non-perfect 4th and 5th intervals are simply encountered much less frequently than other intervals (with the exception of the tritone between the 3rth and 7th of a dominant V chord, the characteristic dissonance that sets up the V-I authentic cadence).