Why wouldn't anybody think voter ID is a good thing? To think voter ID is bad would be just silly...or subversive.
Why is a matter of history - in the reconstruction South, until the early/mid 20th century, there were various qualifications placed on people voting, particularly a literacy test or poll tax. The intent was to prevent black people from voting, since with segregation they could keep some black people illiterate and poor. So they couldn't pass the reading test or pay the tax. It was 100% unequivocal racist in basis. I can't speak for anyone else, but that was wrong and I am glad that this was outlawed. IT wasn't entirely ended until the Civil Rights Act of 1964, passed over the strenuous objections of leading Democrats by Northern and Midwest Republicans on moral and constitutional grounds - the same groups/positions that were in contention over abolition.
The same argument is now made for voter ID laws, particularly government ID, as discriminatory. Of course in this case, it is legitimately discriminatory, in that it is intended to discriminate between legitimate voters/citizens and illegal immigrants. But the same argument is made, that having a government ID is too difficult and discriminates against (citizen) minorities.
Of course only the most dimwitted, or those with an ulterior motive, can draw an analogy in these two things. You have to look at who these arguments favor to see what their motives are. Allowing illegal aliens to vote in a US election is literally suicidal, and I happen to believe that the constitution is not a suicide pact.
An interesting historical fact is that the same group culpable in the first case (i.e. the Democrat party, formed to try to support the cause of segregation and white supremacy {with the KKK as the militant branch}) is using their previous misdeeds to perpetrate this misdeed, in this case, again, to attempt to illegally sway elections in their favor by allowing and even encouraging/facilitating voter fraud. In several states they have already managed to pass laws to permit convicted felons to vote (already swaying the Virginia presidential election in favor of Grandma Cankles herself in 2016).
There's a lot more to the line of reasoning than mentioned here (for instance, how can a man who was not just in the KKK, but a leader in the KKK, vociferously argue against the Civil Rights Act in 1963/64 and then presto-chango, be a leading member of the Democrat party and arguing that his ideas are to favor minorities a few years later while voting for the Neo-Segregationist "Great Society" program?) but you get the gist.
Brett