What is the difference between the sentences "I can't do this" and "I can't be doing this"?
"I can't do this" is in the present tense and it has an enduring aspect, i.e., it's the statement of an ongoing truth. Suppose you've never cooked an elaborate meal before but have committed yourself to cooking a five-course meal for twenty people. In the middle of a kitchen that's a complete mess, you say to yourself
What was I thinking agreeing to cook? I can't do this.
You mean literally that you are unable to perform the task.
"I can't be doing this", on the other hand, is in the present progressive, and it refers to some particular action that is ongoing right now, and it has the connotation that you're doing something surprising that you ought not do, even though you're actually doing it. From Coming Apart: Why Relationships End and How to Live Through the Ending of Yours by D R Kingma
Another form of “This can't be happening to me” is, “I can't be doing this. I can't be ending my marriage. I can't be walking away from all this—from my wife, my house, and my kids. This isn't me. I can't be doing this. Other people are cruel and crass and mean and selfish enouigh to walk out on their marriages. Not me. I'm a nice person.