Can "female"/"male" be insulting?
Solution 1:
I think the issue in your link is referring to people with the terms "a female/females" or "a male/males," used as nouns rather than as adjectives. This can sound somewhat clinical or reductive.
If you Google the term "feeemales" (which represents a stereotypical pronunciation of this) you'll find people generally use it when trying to parody misogynists/clueless sexists.
The words "male/female" are generally not taken as offensive when used as adjectives to refer to body parts, conditions or ideas associated with human men/women. (Examples: "the male/female body," "male/female voice," "male/female depression")
When referring directly to men or women, there is sometimes a choice between using male/female as adjectives and using man/woman as noun adjuncts. Using a noun seems to be more common for women than for men (see this question for more details: Female adjective re job title). But in general, using the adjectives male and female should not be offensive, provided that there is a reason for mentioning the person's sex at all: phrases like male authors and female authors are commonly used.
I also found a Reddit post by someone who claims they find the word "feeemales" "repulsive." Not a good source for grammatical analysis of the word, so just ignore all of that, but it's a source that shows that this attitude you've noticed does exist.