As I see it, there's nothing offensive about "do better" - it's just asking the person to not repeat the same (ostensibly misguided) thing they did before.
On the other hand, there's Kratos's “Don't be sorry, be better”, which did hit me hard when I reached that part in God of War 2018. That one hit me on a very personal level.
"Do better" when used in an online debate forecloses discussion. It implies that the one saying "do better" is the authority on what "better" is. What if I disagree?
Then you reply with "Because of the following reasons, doing better must entail the following actions...", rather than argue against the need to do better
It's annoying in the same way gish gallopping is annoying: you're giving me nothing except resistance in a way you've formulated to appear as though it's in good faith, even though it's not.