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I am on Telegram you can delete a conversation, there should be a pop up and a query asking if you want it deleted for the person whom you are speaking with, if you leave the box unticked it will only delete it for you but the whole conversation will be available for the other person. With all that said, if a person is getting "offended" over a deleted conversation then the problem lies with that person.
"Offensive" isn't the word I'd use, but I can see how I might feel it was rude.
To be frank, I really really wish I *did* have transcripts of my conversations with friends even from in-person. I have a garbage memory and it's really embarrassing that I blithely start retelling stories to the same person -- or refer to something major in my life that they never knew about! Just using encrypted messaging where I can't neatly search the full history already hampers my habit of trying to check if I've said something before. I know most people wouldn't, but....
I can't imagine blocking someone if they cleared a message archive, but I would expect it to be mentioned -- like "ah, nothing's up, I'm just tidying my message histories" or "oh dang, sorry, hit that by accident".
It's a feature of Telegram, so it's clearly intended to be voluntarily ephemeral from both sides. On the one hand, I like having archives of conversations to look back on (just in case), but on the other hand...if they blocked you over something this inconsequential, I don't think their conversation was worth maintaining, anyway.
I think the expectations are different for IM vs in-person spoken conversation. Also, when you deleted the conversation, you probably deleted it for the other person, too—and I wouldn’t be surprised if Telegram didn’t make it easy to export conversations as plain text for archival.