As the sibling commented, there's really no proof to feeling. You can remark that something reacts to the environment. And we can use sophisticated tools to approximate things (e.g. brain MRI can see which parts of the brain "light up" in response to certain things).
I don't know of any way to prove feeling. It seems like a solipsistic trap. I _believe_ that most animals "feel", and _believe_ that no plants/fungus do...but it is merely belief that I don't think to be testable.
I do get the argument, but I do believe it's a pedantic point that's being taken a bit too far. The topic is still worth discussing, without giving up because there's a theoretical point that we cannot prove the causality.
We can start out with the assumption that humans can feel, since ourselves experience it, and can relatively safely transfer this to other humans (who exhibit all the subjective external signs of feeling, which seem similar to our own external signs when we are feeling things). We can also isolate the physiological properties which seem to play a role in this; say, a nervous system, or particular brain characteristics or region activations. This can be further evidenced by cases where individuals lack these, and lack the external signs of the feeling.
So if you then take a physiologically highly related and similar animal to a human, which also shows the external signs of feeling, I believe the argument that it is NOT feeling would be the option that is more absurd, and requires more proof than the argument that says it is feeling.
Of course, this rapidly falls away when we argue about very different types of creatures (say, fungi), or when theorising about types of feeling that might be possible, but we do not have, but nevertheless the entire topic is not worthless, IMHO.
I don't know of any way to prove feeling. It seems like a solipsistic trap. I _believe_ that most animals "feel", and _believe_ that no plants/fungus do...but it is merely belief that I don't think to be testable.