Why are some scale degrees avoided? What is the reasoning behind the avoid notes? Are there avoid notes in all modes? If so, which are the avoid notes of the different modes? Is this pattern widely spread through Jazz?
An avoid note is a chord tension which creates an interval of a minor ninth (or less) above a chord voice. Chord voices are the 1, 3, 5, and 7. Chord tensions are the 9, 11, and 13.
As I recall, the Imaj11 sounds terrible. On the other hand, the iimin11 is fine (because of the b3). Ditto the vimin11. And the IVmaj#11 sounds fine as well.
The avoid notes are fine in passing and arpeggios, but they are not necessarily agreeable in harmony. I have charted them here. The avoid notes are indicated in red; the affected chords are highlighted in yellow.
Here are some examples:
I'm sure more comprehensive and insightful answers will come, but it is common knowledge in jazz I would say. The reasoning is that the avoid tones clash with come of the commonly played chord tones. One example is the fourth of the major scale, when used over the I chord, since it clashes with the third (it's a minor 2nd between them). For C the third of the chord is E, while the fourth of the major scale is an F. It also creates a tritone with the 7th B. According to a survey mentioned in the Lydian Chromatic Concept of Tonal Organization, most people find the Lydian scale the most pleasing over a maj7 chord. Since the 4th is raised, the avoid tone is avoided in the Lydian scale. (It does create a minor 2nd with the 5th though...).
Avoid tones doesn't mean "never play", but rather "use sparingly or as passing tones". The patterns emerged since people disliked the sound of these notes together with the accompaniment.