The word anchor baby is offensive because it cast judgement on the motivation of a child's birth. A presumption is made that the child was born for the purpose of gaining immigration status. That may be true in many cases, but it presupposes the motivations of religion, procreation and simple nature are not the parents motivation for procreating. It stereotypes both children and parents.
Parents come here illegally (drop anchor so to speak) and have a baby who is automatically a US citizen (baby).
Anchor baby is exactly what they are. I don't give a shit about their motivation ... they're here illegally, they shouldn't get a free pass, I don't give a shit if they're offended. If they're so offended they can leave and come back the right way. Problem solved.
It isn't you we are discussing. It is a guy running for President. He shows ignorance and blames it on not caring about political correctness and his flock follows him.
You show your ignorance by claiming people are here illegally. Babies are born while the mother is here on student visa's, work visa's, tourist visa's. A girl here on a "green card" that allows her to work here for two to ten years can be the mother of what are being called "anchor babies".
So, it does't matter what you think, you have no real knowledge about the topic and you aren't giving a rational or even intelligent idea of how to solve the problem.