It's not the opposition to the arrest of wanted criminals (or suspected criminals) -- it's opposition to airports being used in a domestic dragnet and airlines acting like cheap government informants.

Add in the likelihood of mistaken identity and that even if there is a wanted criminal, perhaps a busy public place like an airport may not be a good place to "pick a fight" or the best place to pick up a wanted criminal or suspect.

Also, not everyone welcomes America behaving increasingly like the defeated Soviet Union of yesteryears -- a USSR that also loved to do all sorts of police operations at airports and train and bus stations.