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I'm not a teacher
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You can use the progressive with some state verbs to emphasise a particular meaning e.g.:
(1) I'm understanding poetry more and more. - I perceive that this process is really going on, I make conscious steps, put some effort in it (the phrase "more and more" is very characteristic here, you could do the same with "gradually").
(2) I think he's liking me more and more. - progress is perceptible
(3) I'm realising it more and more.
(4) Now after the semester I'm hating it more and more.
(5) Now, with discovering of new documents, we're knowing more and more about the period.
(6) What are you wanting? - for example in a situation where a group of people can't make up their mind about what to order in a restaurant.
With verbs see and hear it's a bit different because they do have their "progressive brothers", namely, look and listen, which suggest that the processes are controlled. However, you can still use 'see' and 'hear' in the progressive e.g.
(7) I'm seeing double.
(8) I'm seeing things. - you're inventing these things, they're not there (that's how it's perceived by others)
(9) I'm hearing voices.
Here the mind of the person speaking is producing those "things" and "voices". It's no automatic perception but rather something abnormal. We cannot control this process but we can be aware that it's in progress.
However: (10) I'm seeing a doctor tonight means I was responsible for making the appointment.
Now let's imagine you've gone to Australia and somebody asks you there: (11) How are you liking it here? It means: how has your opinion changed over time? No spontaneous expression is expected but observations concerning the change. Another way to paraphrase that would be, "have you progressed in your appreciation of this country?"
You can also use the progressive with verbs like like and love to emphasise this liking/ loving is perceptible to others:
(12) She is loving every bit of attention she is getting. (Let's say she's the mum of the year, people are congratulating her, and it's physically visible how she's loving it, maybe she's blushing, smiling etc.)
(13) He's loving every bit of his victory! Look at him.
(14) They are liking every single moment of it! - they like it and it shows
Other examples:
(15)Thinking of the beliefs you believe in, you are believing.
(16)We are believing! Because we see our prayers answered. - the results are perceptible
(17)They're placing more value on things that are mattering less (and less).
You're translating for an English guy in a business meeting. He wants to close the deal but the other party seems rather reluctant to do so, and he finally asks you: (18) What are they wanting? (which means the people are inventing artificial obstacles)
(19) You're being nice. - you're behaving in a nice way OR normally you're not like that, but now you are and it's surprising.
(20) They royal visit is not being a success. - the visit's not over yet but so far it's not very successful.
(20) I'm forgetting something. - uttered upon walking out of the room; you realise you're in the middle of the process. Normally we can't follow the pace of it but sometimes you can get the sensation that indeed in the very moment you're forgetting about something, it becomes perceptible for a split second.