Yet again, curvature is a quantitative concept relating to geometry (distances, angles).
It is a property of an abstract sphere, an (approximate) real sphere, an abstract Riemannian manifold and real space-time, having a similar description in all cases. In all these cases it is a proposition about the geometry, determined by observable quantities in the real-world cases of an (approximate) real sphere and space-time.
It is a typical example of the power of mathematics that closely related concepts apply both to the elementary spherical surface and to space-time, but the key thing is that the observed distances in space-time make it impossible that it is flat (just like distances on a sphere make it impossible it is flat, even if you had no other information but these distances).
There is no "control" here. I cannot improve your understanding at all - only you can, or choose not to. My point is that the former is more to your benefit and you shouldn't leave yourself worse off on my account.
There is a problem that you view it as "unfriendly" for me to point out that it is objectively true that space is curved (i.e. not flat) and to point you towards someone who is far and away more authoritative than me to explain it (much better than I could). There is no more unfriendliness in this than in a move in a chess game (good or bad). But note that my objective is _always_ to get closer to the truth, and I am never willing to compromise that for a petty debating point.
Maybe my understanding of some of the fundamentals of cosmology is better than yours though, and you're deceived into thinking yours is better, perhaps because you are distracted by too many details, so you can't do the big picture. I don't consider it "unfriendly" for you to point out what you subjectively believe is objectively true, if you do it properly and well. Your obvious hostility and controlling behaviour, however, has been of your own making. Perhaps you can't help it and it isn't intentional but I get on well with everyone who behaves well and has respect for all others, as I try to do also. Perhaps you allow the wrong people to influence your behaviour but you passed a point quite recently where I decided that enough is enough.
Your last sentence might easily mean that you will never compromise a petty debating point in order to behave in a more friendly or decent way to others. It seems that it does mean that; or should mean that.
It is not "subjective" that space-time is curved. Remember this is a proposition about the relationship between different observable quantities, testable by experiments making appropriate measurements. This is how the scientific method tests objective propositions.
There are precise experiments that make the measurements that confirm curvature of space-time. A remarkable example was the recent one that demonstrated gravitational time dilation over a height of less than 1 mm in the Earth's gravitational field - this is an effect billions of times smaller than the curvature of space on a planetary scale, itself very small because the Earth is not very massive! The anomalous precession of the orbit of Mercury is likewise due to the curvature near the Sun. (This would be a lot simpler if there were only one planet, since Newton's laws cause precession due to the force between planets)
The fact that light is deflected by masses despite its lack of mass is a consequence of curvature. In flat space-time, you can't get gravitational lensing at all: if two beams of light come from the same point, they can never bend back together, because straight lines in Euclidean space can't cross twice.