The reason they get called "illegal" is that they "aren't legal" in one relevant sense.
It's sort of like the difference between "immoral" and "non-moral:" A chair isn't moral, because by itself it can't be moral or have any property of being moral. However, you don't say that it is moral or immoral - it's non-moral. But like that, a person by themselves can't be "illegal" - the idea of a person being illegal is contrary to the spirit of the Constitution, even for non-citizen aliens, and it probably isn't intended by people who use the word, either.
The phrase "non-legal" would probably be interpreted much the same way as "illegal" is, though, so that probably wouldn't help much. It also doesn't make clear in what sense they lack legal status. It is clear that they do have some legal status - just not the relevant legal status of being documented and having a status of permanent residence.
Removable or deportable are interesting terms which seem to capture the relevant points, so it seems alright to me.
p.s. "Everything I like is illegal, immoral, or fattening"
antron wrote:The recent supreme court decision on a state's right to treat them as criminals led to much hilarity. Arizona Governor Jan Brewer celebrated that morning because it upheld her right to check someone's immigration status if being held under suspicion for an actual crime. That afternoon Obama disconnected Arizona from the federal database that police use to check such a thing. That evening she was back on TV and furious.
I know there is more going on than that, but it's been a while and I've forgotten some of the relevant details. It seems to me that there isn't a problem with checking a person's immigration status if they are being held under suspicion of an actual crime. I know the argument is out there that people will get pulled off the streets for this end, but police already abuse minor traffic violations as a pretext to stop a vehicle and then use that proximity to engage in "probable cause" searches. Nobody seems to have a solution for that, and nobody wants to revoke that right because it would be ridiculous to forbid police from a probable cause search merely because they accidentally bumped into a perp in some other context. I guess the difference must be that probable cause searches allow police to intercept an actual crime, whereas an immigration check does nothing of the sort because merely being a removable alien in the country is not a crime.