Yes like Ted said, with these idiomatic sentences about how people are doing it helps to think of the sentence as translating to: It goes the student good. As in, 'it = life' and life is treating the student well, thus the student is the object being acted upon by life and thus it's dative.
Hope that makes sense :)
The use of "with", I feel to be far too ambiguous to be a clear English construction, but I have heard this "with" usage, now and again, over the years.
The problem is, you could be saying something is good when it's with the students, similar to this sort of usage: "Chocolate goes well with ice-cream".
I'm speaking outside of this specific question for Duolingo; they seem to want "fine", but I imagine other variations of "fine" would be accepted.
EDIT: Actually, I'd say "for" would be far better to use than "with"; I just personally find it sounds odd, with some sentences, but it is actually used and does make sense, grammatically. "Things are going well for me, thanks for asking."
Ihnen geht es gut. = It goes well for them. (or "you" formal, plural or singular, I think)
Ihm geht es gut. = It goes well for him.
Ihr geht es gut. = It goes well for her.
Mir geht es gut. = It goes well for me.
Dir geht es gut. = It goes well for you. (informal, singular)
I'm not actually sure how to use the informal plural for "you". Sorry if this is rusty or wrong - I rarely ever use the Sie form and I rarely talk to more than one German person at a time, so I don't get many opportunities to practice either usages. :|
EDIT: Did some looking, and I think that last one is "euch", for plural, informal, "you". "Euch geht es gut." I thought it was just the plural version of "dich", but apparently it can be used in the dative, too.
This helped me:
Hope that helped.
Ich würde froh, wenn jemand mir korrigieren kann oder noch mehr darüber sagen
"Den Studenten geht es gut." I think. Or "Es geht bei den Studenten gut." From what I've seen, the "bei" is optional, ... I just added it out of habit. "Die Studenten sind gut." is probably another way to say it, although I think that would be less used. Not 100% sure about all that, though.
Nooo, this is an old post of mine. ignore the: "Die Studenten sind gut." that is absolutely wrong. xD That means the students are good, as in good people or summat. xD What was I thinking.
although it looks like it's being marked as a masculine, accusative noun, it's actually being marked for plural in dative, which also has the article 'den'. The reason it is dative is because in sentences with this 'geht es' or 'es geht' construction, the 'es' is doing the action to the students and the students are the indirect objects. In other words, 'IT is GOING the students good'. However German doesn't even need to write the words in that order, it can write 'the students GO IT good' as it has essentially done here, because the dative personal plural pronoun 'den' shows that the students are the objects.
A simpler, more obvious example of how this is dative comes from another discussion post: "Mir geht es gut" translates to "I am fine", and as you know, 'mir' is a dative personal pronoun. Here's the link, hope that helps. :) Kat https://www.duolingo.com/comment/187798