Why did Obama use "children" over "fetus" to describe the unborn?

Dan Gilgoff spots something interesting in Obama's ND speech:

One line in particular in President Obama's Notre Dame speech really jumped out at me: "Let's provide care and support for women who do carry their children to term."

Obama used the word children as opposed to fetus, employing the nomenclature of antiabortion activists as opposed to that of the pro-abortion-rights movement. If the fetus is a child, antiabortion advocates say, how can you justify abortion?

... Is the president subtly invoking the antiabortion lexicon in addressing conservative religious audiences? Or am I reading too much into this? (US News)

I have to respond that, sadly, I think Gilgoff is reading too much into this.

You see, abortion advocates are happy to use the term "child" to describe a "wanted" child. In other words, for them, a child is not a "child" until the mother has made a choice to keep it. Otherwise a "child" remains a "fetus" until he or she takes their first breath of air.

What changes for that child at that moment - besides location - escapes me, but so goes the illogical logic of abortion supporters.

Besides, Obama spoke about his desire to eliminate "offending" words from the public discourse on abortion (funny that he chose a term commonly used against pro-lifers - "ideologue"). Can one imagine how jarring it would be, considering the audience, to have called an unborn child a "fetus"? Especially considering how often the word is used in the phrase "terminate a fetus"?

I would hope somewhat jarring.