Asking for forgiveness is difficult, so most of us have learned to do it without mentioning what we actually did. Mistakes were made, things were said, and nobody is entirely clear on who did them.
I have apologised many times without ever saying what I was apologising for. It works surprisingly well, which is part of the problem. Arjuna does it properly, which is uncomfortable to watch.
He has just been shown the universal form, and he is badly shaken. What he apologises for is oddly small. He had called Krishna by his name, casually, the way you talk to a friend. He made jokes at his expense. He was careless with him at meals, while lying around, while sitting together, sometimes alone and sometimes in front of other people. He goes through it occasion by occasion, a man reviewing years of friendship for anything that might now be a problem.
Anybody who has worked out mid-sentence that the person they were teasing is considerably more senior than they had assumed will know the feeling.
तस्मात्प्रणम्य प्रणिधाय कायं प्रसादये त्वामहमीशमीड्यम् । पितेव पुत्रस्य सखेव सख्युः प्रियः प्रियायार्हसि देव सोढुम् ॥
tasmat pranamya pranidhaya kayam prasadaye tvam aham isham idyam piteva putrasya sakheva sakhyuh priyah priyayarhasi deva sodhum
So I bow down and ask for your grace. As a father with his son, as a friend with a friend, as a lover with the beloved, please bear with me.
The word at the end is sodhum, to bear, to tolerate, to put up with. That is his final ask, and it is a much smaller thing to request than absolution.
He gives three pictures of what it looks like: a father with his son, a friend with a friend, somebody in love with the person they love. What those three have in common is that nobody is leaving. The relationship carries on regardless of the offence, and the apology is made within that.
Most of my apologies are requests for a verdict. I want somebody to tell me it is fine, ideally within the hour, so that I can put it down and go back to being a pleasant person. That is quick, and it is mostly about me.
Arjuna asks for something slower. He names every occasion first, then asks only to be tolerated.
Next time I owe somebody an apology, I am going to write the list first and see how far I get before I start editing.