You are getting downvoted because it's completely unclear why the term "broken english" is offensive or not fit for use. You also did not propose an alternative.

I promise my use of it was entirely descriptive and not at all a judgement of the person speaking it. I have the utmost respect for anyone who can communicate an idea in another language at any level. I see my self as deficient for not being able to do so and think of myself as lesser and a poor citizen of the world for only speaking english.

The term broken means something was once whole and is no longer. There's plenty of alternatives like non native speaker, beginner speaker, etc. I'm generally extremely non PC but this one is a pet peeve of mine.

As a native English speaker living in Russia, it really made me realize how difficult and nerve racking language learning and speaking is. I don't consider my Russian skills "broken", just very incomplete; a WIP.

Broken in the sense "broken line" (https://duckduckgo.com/?t=ffab&q=broken+line&ia=web); not "once whole", rather "with breaks (pauses/gaps) in it". Like when a conference breaks for lunch, it doesn't mean the conference was whole and now is inferior.

How could I who learned English after childhood strive for greatness without distinguishing real from broken, i.e with potential for repair?

There is nothing that is equal in this world