"Foreign students" vs "International students"

Solution 1:

The primary definitions of the word "foreign" in the American Heritage Dictionary and the New Oxford American Dictionary are definitively neutral, yes.

International: AHD:

Located away from one's native country.

Of, characteristic of, or from a place or country other than the one being considered.

NOAD:

Of, from, in, or characteristic of a country or language other than one's own.

But their secondary definitions bring associations or connotations that many persons might not wish associated themselves.

Foreign: AHD:

Situated in an abnormal or improper place in the body and typically introduced from outside.

Not natural; alien.

Not germane; irrelevant.

NOAD:

Strange and unfamiliar.

Solution 2:

(1) The trend towards more frequent use of ‘international students’ is driven by bureaucratic usage. Most universities in the English-speaking countries have some kind of an office with several full-time employees that caters to such students, and such offices have been becoming larger and more influential over the recent decades (together with other university offices devoted to ‘student life’, as distinct from actual instruction). The people who work in these offices now see it as a part of their professional identity to always use the term ‘international students’ instead of ‘foreign students’, and to insist that such terminology be followed in all official university communications. Most ordinary people only rarely need to use either term; when such an occasion arises, they may nowadays choose to use ‘international students’ because they remember having seen it on their university’s website. The increase in the use of ‘international students’ thus probably hasn’t arisen through spontaneous developments in the everyday use of the language.

(2) Software of the kind referred to in the question is probably not used by those who genuinely care about their style of writing and the more subtle nuances of meaning. On the other hand, it is likely used by the people to whom such matters are not important in themselves, but whose jobs require them to quickly churn out memoranda that will look O.K. in the eyes of their employers. It is thus understandable that such software will be biased towards bureaucratic usage.

(3) Given that the word ‘foreign’ simply means from another country, it is unclear why anybody who actually is from another country would be offended by being so described, unless there is something about the context that makes it offensive. One can imagine a context in which the word is used to suggest that the person is an outsider who doesn’t really belong here, and that would, of course, be offensive, but in such cases it is not the word itself that is offensive but the combination of the word and the context. And in such a context, the word ‘international’ would probably be offensive too.

(4) As has already been pointed out in the comments, the words ‘foreign’ and ‘international’ are not interchangeable. The term ‘foreign student’ conveys the idea that one’s domicile is in another country; the term ‘international student’ conveys the idea that one’s studies are a part of interaction (exchange, cooperation) between the two nations. It is true that when one label is applicable, the other one is usually applicable as well, but they still direct attention to different aspects of the person. Many people choose to study in another country because of the quality of its schools, and of how that quality contributes to their individual self-improvement; they do not care that their doing so may also be regarded (by somebody else) as a part of some grand scheme of cooperation between the two nations. Insisting on the label ‘international students’ may be casting them into a role that they do not particularly identify with.

Solution 3:

Foreign can have a connotation of strange or out of place. Think of a foreign object in terms of something that doesn't belong where you found it ("he choked on a foreign object").

It's similar to how "illegal alien" has an offensive connotation ("it's not a human, it's an alien!") whereas "illegal immigrant" is a more neutral description.

Solution 4:

The use of foreign would indicate a relationship relative to a host. Whereas international is a more objective descriptor.