Why does an authentic cadence sound pleasing to the ear? What makes an interval "Consonant" or "Dissonant" and why are there only two categories for intervals?
The notion of consonance/dissonance depends on the tradition or style used.
In European common practice perfect unions, octaves, fifths and major/minor thirds and sixths are consonant while seconds, fourths, tritones, sevenths and imperfect intervals are dissonant.
Some try to explain that arrangement acoustically by calling simpler ratios being more consonant. So an octave's ratio is 2:1 simpler and more consonant than a minor sixth with ratio 8:5.
The perfect fourth is interesting in this context, because sometimes it is considered dissonant other times consonant.
This doesn't explain the part of your question about perfect cadences. But that is a different question.
I would caution against thinking of intervals fitting into only two categories. There are several other categories/descriptors which can be reviewed here https://en.wikipedia.org/wiki/Interval_(music).
Perhaps you meant: why is there only a two-part consonant/dissonant duality? Some things can be though of in a dualistic way - light/dark, inhale/exhale, up/down, etc. - but sometimes you can or should reject dualistic thinking. There is music that doesn't work around notions of consonance/dissonance.
Intervals aren't necessarily consonant or dissonant in themselves, it depends to an extent on where they are and what they're doing in the music.
There are not only two intervals per se. There are major, minor, augmented and diminished in most music.
It all depends on mathematical relationships. An octave is easy on the ear since it is a 2:1 relationship. A fifth likewise is an easy fraction. A third is more complex and thirds were for a long time considered dissonant. Then along came the 'consonance Angloise' and thirds became acceptable as consonances. Minor seconds have a relationship that is hard for the auditory system to analyse or relate mathematically so are heard as dissonant. It's all about the harmonic series.
The "consonance" and "dissonance" relates to how the interval sounds like.
Here are perfect consonance intervals. They have a very good and a bright sound.
- Perfect unison
- Perfect 4th
- Perfect 5th
- Perfect octave
Here are imperfect consonance intervals. They have a "mild" or a "neutral" sound.
- Major 3rd
- Minor 3rd
- Major 6th
- Minor 6th
Here are dissonant intervals. They basically do not have a good sound. Please note that ALL augmented and diminished intervals are dissonant. Any chord that includes one or more of the following intervals are considered to be dissonant.
- Major 2nd
- Minor 2nd
- Major 7th
- Minor 7th
- Augmented unison
- Augmented 2nd
- Augmented 3rd
- Augmented 4th (Tritone)
- Augmented 5th
- Augmented 6th
- Augmented 7th
- Augmented octave
- Diminished unison
- Diminished 2nd
- Diminished 3rd
- Diminished 4th
- Diminished 5th (Tritone)
- Diminished 6th
- Diminished 7th
- Diminished octave