Burt Likko does not want to hear about dismantling the system. That's ok. I don't think the speakers wanted to talk to him.
Likko doesn't really give any actual reasons why Black Lives Matter shouldn't want to dismantle the system. His only "argument" is that he has at least some standing as an ally: he agrees that black people shouldn't have to worry about being shot by the police, and he's done a lot of civil rights legal work (presumably he's an attorney). As an ally, he doesn't like their goals.
However well intentioned — and Likko does seem well-intentioned — he's engaging in pure concern trolling.
First, he has no right to declare himself an ally of anyone. Allies are chosen by the principals, not the other way around. If BLM wants him as an ally, they'll ask him. Similarly, while I stand behind BLM 100 percent, I do not declare myself an ally, and I don't presume to advise them their goals, strategies, or tactics.
Analysis is a different matter. If Likko wanted to talk about actual reasons why he doesn't think BLM should want to dismantle the system, it would be entirely appropriate (IMnsHO) to talk about those reasons. But he doesn't.
I happen to agree with the speaker Likko cites: racism and the police murder of black people are so deeply baked into American capitalism that they have become nearly inseparable. If you think that the police can be reformed without dismantling the capitalist system, you don't need to cajole BLM or its representatives into not calling for dismantling the system; all you need to do is actually, you know, reform the system. Good luck with that.