If someone asks me if I want to go to the cinema, I might say that 'I don't want to go to the cinema'. But it's not that important. 'The last thing I want' means 'the thing I want the least'. So, there is more emphasis on 'not' wanting something. For example, if I am on my way to a job interview, 'the last thing I want' to happen is for the car to break down, because it would make me late. So, we usually say 'the last thing I want' when we are talking about something that would be a bad or unpleasant thing or something that we definitely don't want to happen. I hope this helps