I am not an expert in philosophy by any stretch so feel free to poke holes in what I'm about to say, but I somewhat agree with the author's points here, assuming we take nihilism to mean "to both believe and feel nothing has meaning". I think the author may have the causation in the first point backwards though. To truly feel like nothing has any meaning, I think you must first be quite miserable - I doubt anyone first chooses nihilism and then becomes miserable because of that choice. Imagine all of your relationships, your career and all of the other things people usually care about feel meaningless - you would probably be miserable and depressed. It is one thing to believe that life is objectively devoid of meaning. It is a different thing to subjectively feel that nothing in life has meaning.
If you accept that a true nihilist has to be depressed, I would agree that the third point follows. Acknowledging a depressed individual's viewpoint that it is okay to feel everything is meaningless - that this viewpoint is not indicative of a mental health issue that should be addressed - would probably erode societies ability to improve the lives of depressed individuals (assuming improvement means they suffer less).
As to whether other people's suffering matters to you or not, I suppose that depends on the individual. The author seems to think it is not ok for people to suffer, but obviously not everyone would agree with them here.
If you accept that a true nihilist has to be depressed, I would agree that the third point follows. Acknowledging a depressed individual's viewpoint that it is okay to feel everything is meaningless - that this viewpoint is not indicative of a mental health issue that should be addressed - would probably erode societies ability to improve the lives of depressed individuals (assuming improvement means they suffer less).
As to whether other people's suffering matters to you or not, I suppose that depends on the individual. The author seems to think it is not ok for people to suffer, but obviously not everyone would agree with them here.