For most of the era people are picturing, there was almost no law to break. Ellis Island turned away about 2 percent of arrivals. Your ancestors didn't follow the rule you're asking for — the rule didn't exist yet.

Until the 1920s, arriving in the United States mostly meant showing up. There were no numerical caps on European immigration, no quotas, no visa queue, no consular interview. Inspectors at Ellis Island screened for contagious disease, criminal record and likelihood of becoming a public charge, and admitted roughly 98 percent of the people who came through.

The category of "illegal immigrant" is largely a creation of the Immigration Act of 1924, which set national-origin quotas designed to preserve the country's existing ethnic composition — and of the restrictions built on it since. Before that, an Italian or Irish or Polish great-grandparent did not immigrate legally as opposed to illegally. They simply immigrated. The paperwork they are remembered for complying with was mostly created after they arrived.

So the comparison is not between an ancestor who followed the rules and a migrant who broke them. It is between someone who arrived when the door was open and someone who arrived after it was closed — and the honest version of the argument is not about legality at all. It is about who got here first.