What was Hevel (Abel's) sin?

Question

The Arizal says that Hevel was reincarnated many times to purify his sin. What was his sin?

Answer 1

See here as a translation from the Arizal:

Cain and Abel also damaged [reality]. [Not only Cain but also] Abel "gazed and damaged".

According to the Sages, when Abel offered his sacrifice to G-d, he gazed upon the Divine Presence and therefore became incurred the death penalty (which is why it was divine providence that Cain killed him). Gazing upon the Divine Presence means experiencing divine consciousness for selfish intentions. The individual considers himself an independent agent who may rightfully pursue his own satisfaction. Having chosen to sunder himself from G-d, the source of life, he forfeits life - even if the object of his satisfaction is none other than the Divine glory!

This is the mystical meaning of the phrase: And G-d paid heed to Abel and his offering (Gen. 4:4). We would have expected this phrase to read: "And G-d paid heed to Abel's offering." The meaning of G-d turning to Abel here is that He allowed him to gaze [on the Divine Presence].

Abel should have demurred, aware that it doing this would cause him to experience G-dliness as one separate from it. Indeed, when Moses realized that the burning bush was a revelation of G-d, he "hid his face, for he was afraid of gazing at G-d." (Commentary of Rabbi Shalom Sharabi on Ex. 3:6.)

Raises the next question of where the reference is to "According to the Sages" but that is another question.

Answer 2

As others, I don't know what the Arizal is referring to. But Kli Yakar says that Kain was the first who made the sacrifice. Hevel envied him and made a sacrifice too.

As a hint to this, he brings a posuk from Kohelet 4:4

וראיתי אני את כל עמל ואת כל כשרון המעשה כי היא קנאת איש מרעהו גם זה הבל ורעות רוח

Answer 3

I don't know what the Arizal is referring to. However, the Chida (in his פני דוד) cites Chaim Abulafia's עץ חיים that הבל instigated the whole affair:

אמרו ז״ל ויקם קין שביקש הבל להורגו ונתגבר קין וקם עליו והרגו ז"א אי הבל אחי־ היה לך להצי׳ עצמך בא׳ מאיבריו ואיך הרגתו השיב לא ידעתי כלו' לא יכילנא ליה השומר אחי וכי יכולתי לשמרו והרגתיו. ועוד תי׳ אנכי הוא דין הרא"ם שהנרדף אינו חייב לדקדק בכך ואנכי הנרדף השיבו הש״ית למ״ש לא יכילתא ליה קול דמי אחיו דרשו ז"ל דם אינו או׳ מלמד שהיה מכה פצעים וחבורות ולא היה יודע מהיכן נפשו יוצאת והייתה יכול לחתוך ידו או רגלו ולברוח ולטענה שהייתה נרדף אפ"ה צועקים אלי תי' אלי ר״ל שבידי שמים תתחייב ונ״מ שאם הרגו גואל הדם פטור כסי בכה"ג מש"ה אמ׳ הן גרשת אותי והיה כל מוצאי יהרגני וישם ה׳ לקין אות לבלתי הכות אותו כל מוצאו כאמור

Is this the sin that the Arizal refers to? I'm not sure.