Mike mostly criticizes cultural evolution's concept of progress.
Evolutionary progress is denied by some cultural evolution researchers (notably Alex Mesoudi) - and is widely denied by evolutionary biologists. I call this "progress denialism". Evolutionary progress is obvious. Evolution is a gigantic optimization process. It seeks the fittest agents - the angels, so to speak. We are some of the first apes who learned to write - and are plainly not yet angels. Consequentially, the existence of progress is not very surprising.
Mike is mostly concerned with progressive unilinear cultural evolution. He says this is value-laden, false and racist. He says it has been used to justify colonialism. He describes it as as "problematic" and "insiduous".
Mike doesn't really attempt to make a scientific argument. Instead he mostly presents anecdotes arguing that belief in progress has led to negative social consequences.
I think this argument is like arguing that metallurgy is bad because guns can kill people. Yes, gun use leads to tragic deaths. However that's just one consequence of the findings of metallurgy.
I don't think there's any credible evidence that the idea of evolutionary progress leads to bad behaviour. If there was such evidence, I'm pretty sure that critics would present it. They seem unable to do this. Of course that doesn't mean that evolutionary progress is a harmless idea - but unless there's a good reason for thinking that progressivism is somehow worse than progress denialism, I don't think the progress advocates have too much to worry about when it comes to criticism on moral grounds.
The truth is rarely bad or evil. It is usually better to know than not to know.