The children of Illegal Aliens are not citizens because their parents and them cannot be rewarded for the crime their parents commited against the laws of this land.
It's like letting the son of a bank robber keep the stolen money that his father gave to him.
The child has no right to profit from any illegal act.
"Category Error"... Popular phrase these days, and with good reason - there's a lot of it going around. I made the same point earlier about a stolen lottery ticket not earning the right to claim the jackpot.