I think Orphan Crow has nailed it. What you seem to be objecting the use of precise language or the use of technical language outside the hard sciences.
Whether a distinction is important or pedantic really depends on the situation.
For example someone might say:
The light of the moon is shining brightly tonight.
And a physicist might respond:
Actually the moon is not a source of light, it is reflecting light emitted by the sun.
Whether that response is pedantic, helpful, playful, annoying or whatever probably depends on a complex set contextual considerations. But whatever the intent or reception, it is nevertheless a meaningful distinction that is being made.
It's similar when a theorist responds to a statement such as "only women bear children" with the observation that it depends what you mean by "woman" and it depends what you mean by "bear children". You may find these precise distinctions and technicalities annoying, pedantic or whatever. But they are meaningful distinctions nonetheless.