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I recently joined an organisation, and after a month I decided to quit gracefully, as I feel it's not a good fit for me. I have been a very genuine person and have never done this before, hence I have some fear discussing these things with my manager.
Since my immediate manager is on leave, I gathered some courage to talk to his manager (i.e. very senior manager), but as we started our discussion I started choking. I told him what I feel about this workplace and had to leave my previous organisation because of the same reason. He listened to me carefully, gave some advice, and told me to discuss things with my immediate manager who would return next week. The main thing is I know that things are never going to change, but I didn't have the courage to say I want to quit before his face as it felt rude to me.
The issue is I can't wait until Monday for discussion as I want to serve proper notice period and time is a constraint for me, because I have another offer which has been waiting for me for month. I will try to push them for another month but fear they won't and then I would have hardly 15 days to join them.
So, coming to my question: should I send a formal mail without waiting for my manager? Is that a rude behaviour? Did I do the right thing by not resigning in the first meeting?