Your questions are on discrete probabilities with knowable objective answers (cards/coins/dice), but the teacher also needs to teach the sense that there are continuous probabilities with fuzzy subjective answers (weather/real life events).
This may be one source of the teacher's frustration: most likely the students are answering the question "what's the probability of rain tomorrow?" as though they are guessing the teacher's password "umm... is it 0.5?", as the teacher has effectively taught them to, when in fact they are being asked to have their own opinion.
For your first paragraph, I was trying to teach a little about probability. For the probability of rain, I mentioned that, and my mention implied the good lesson there: We can assume that there really is a probability of rain, that is, it definitely exists. Now, especially for deciding to place a bet, we could get an estimate of that probability. The 50% is a first cut estimate with some curious properties about 'total ignorance' but otherwise poor. So, how the heck to get an estimate? Likely the best practical way was by the student seeing a weather report on the news. Otherwise, for, say, the probability of rain of any day in, say, August "We might, what, class?
Anyone? How might we get an estimate of that? ...?"
Or, "Billy, what company makes iPhones? Billy, you can't get the answer by teasing Sandra. Mary? Right, Apple! Okay, suppose we buy 100 shares of Apple stock today and sell it seven days from now. What is the probability we make over $1000? Assume that this probability exists and we want to estimate it. People especially good at such estimates can become among the richest in the world, fairly quickly. So, how might such an estimate be made? Information? Any ideas? Anyone remember the motorcycle, airport, and airplane in the movie 'Wall Street'? What was the role of 'information' there for an estimate of the probability that the stock of the steel company in Pennsylvania would go up a lot, soon? Anyone? Sandra?"
This may be one source of the teacher's frustration: most likely the students are answering the question "what's the probability of rain tomorrow?" as though they are guessing the teacher's password "umm... is it 0.5?", as the teacher has effectively taught them to, when in fact they are being asked to have their own opinion.