Against He specifically, the biggest factor that causes consternation is that He seems to have been more motivated by winning the accolades of being first than by actually doing good work. The work came out of nowhere, wasn't exactly successful (in that neither of resulting gene edits actually reflected the intended result), and it's unclear if the parents actually understood what they were consenting to.

To the broader topic, one of the major issues is that genes are nowhere near so cut-and-dried as they are portrayed in science fiction. Rather famously, the mutation that confers sickle-cell anemia also confers resistance to malaria. But for most genes, we don't know what the side-effects of their mutations will be. How can you properly ask for consent to a procedure whose consequences are often unknown and perhaps unknowable? All the more harder when the person on whom the greatest burden is borne is not yet in existence, let alone capable of giving consent.