Which implies that without the MCAS, it IS inherently unstable in certain situations. Am I wrong about this ?
As I understand it -- and bear in mind that I know no more about this than anyone who's been following the story on public sources -- yes you are.
The engines of the 737 MAX are larger than those of earlier 737s, and they have to be positioned further forward and higher up than the engines of other 737s to give enough ground clearance. One result of this is that the plane tends to point its nose upwards when the engines are working hard. This is apparently not unusual behaviour for an airliner, and does not mean that the 737 MAX is unstable or impossible to fly -- but it does mean that it handles rather differently from earlier 737 models.
The function of the MCAS system is to compensate for this tendency of the 737 MAX to point its nose upwards while climbing just enough to make it behave like an older 737, so that pilots who are qualified to fly the older 737 can fly the MAX with minimal extra instruction. This is a big deal for smaller airlines as getting a pilot certified for a new airline type is time-consuming and expensive -- MCAS means that the 737 MAX is regarded as the same "type" as older 737s, and makes the plane more attractive to airlines who don't want to have to retrain a lot of pilots.
When it works, MCAS works well, and pilots trained on older 737s can fly them just fine. When it doesn't work the results can be catastrophic. The main problem is that MCAS relies on a single Angle of Attack sensor (even though the plane has two) to tell it when the nose is pointing too high, and when this sensor fails it takes over the plane in a way that is difficult for the pilots to override, even if they do recognize the condition and respond appropriately.
Ideally, Boeing should just admit that the 737 MAX isn't a 737, remove MCAS, and require all pilots who are to fly the thing to obtain certification for the new aircraft type.
I don't see them swallowing that much humble pie, though, so what they need to do to make the 737 MAX safe and keep on pretending that it's just a 737 is to make MCAS use the readings from both sensors, and hand control back to the pilot if the readings don't agree. Ideally there should be at least three sensors of different types, so that if one sensor fails the computer can tell which one is wrong and work with just the other two. The sensors should be of different types to reduce the chance that two or more will be affected by some systematic failure and both give the same incorrect reading at the same time. Boeing also need to make it easier for the pilots to disable MCAS if/when it malfunctions, without having to switch to entirely manual control as they do at present.
The BBC have a reasonable summary here. See the "What is MCAS" section about half-way down.