The worst part is when the left comes up with slogans that don't represent what they said they meant but then they act like they believe the slogans.

"Defund the police" did get police budgets lowered in quite a number of places (mostly without a correspondingly large and effective increase in social services budgets).

Or "check your privilege", which was supposed to mean "be aware that others, unlike you, face unfair disadvantages based on their race", but because of linguistic ambiguity ("check" = "hand in" and "privilege" = "a benefit you don't deserve") tends also to be used as a belligerent attack meaning "leave behind your idea that you should be treated well".

I'm not sure it's universally an innocent blunder. I think some people on the far left actually think the police are superfluous and harmful, and should be abolished, and even no replacement is better than the status quo. The people who first started using "check your privilege" have heavy ties to critical discourse analysis, which means that either they are the most inept students of the field ever, or they know very well that the ambiguity lends itself to a weaponized phrasing and weaponization was the intent.

Both the left and the right have two contradictory goals: goal number one is popularity (and therefore votes), but goal number two is cohesion (and therefore turnout), and nothing boosts cohesion better than having some other group hate you.

So, anyway, I partly agree with you: I agree that persuading the center is how the political future of the country will be decided.

But I have difficulty believing it's all just about the left being inept at messaging. The right is better at it. "Stop the steal" is very catchy, even if the idea it promotes is utterly wrong. But sometimes I think the phrasing reflects intent that does not appeal to the center at all.