While I do not have experience with "Chinglish" in specific, I can speak more generally on the subject of "pidgins" which would include Chinglish alongside Engrish and Spanglish (and many many others). A pidgin is a simplified sort of language to facilitate communication between speakers of different languages who are not fluent with each other, and typically has elements of both languages being used, often using the vocabulary of one language with the grammar of another language, or the pronunciation rules of one language applied to the lexicon of the other. That sort of thing.
You object to your sentence being called a pidgin, and rightly so, as you have not simplified your language to facilitate communication, but rather intelligently borrowed a single vocabulary word from Chinese to make a rhetorical point in perfect idiomatic English, something that native speakers do on an occasional basis themselves... albeit, typically without using an entirely different writing system in the middle of the sentence.
That's the crux of why you've been accused of advocating "Chinglish", by the way: it's simply the mixing of the two writing systems within a single sentence. This is a feature of pidgins-- using vocabulary from one language while speaking mostly in the other language-- so it's easy to see why you might have been misunderstood.
One way you might avoid the accusation, justified or not, would be to avoid using Chinese characters in the middle of English sentences. Instead, if you want to make the same rhetorical point, you could use a transliteration of the word you want to borrow but write it in italics, such as "Yīngyǔ"1.
However, I suspect that your accusers would not be happy with this alternative either, as I suspect they are already fully aware of what 英语 means and sounds like. They just want you to stick to one language or the other, and not mix them at all. They are wrong, but it sounds like this is what they want.
1: (using Google Translate set to Chinese (Simplified))