Foreign students temporarily present in the United States in F-1, J-1, or M-1, status for less than 5 calendar years are generally nonresident aliens under residency rules of IRC section 7701(b).
In which case(s) is a foreign student temporarily present in the United States in F-1 status for less than 5 calendar years not a nonresident aliens under residency rules of IRC section 7701(b)?
The rule is that people are not exempt individuals while on "student" status this year, if they have been an exempt individual for any part of 5 previous calendar years, ever in their life. So you have not consider not just the current stay, but all previous stays in F and J status as well. (And keep in mind the rules for exempt individuals as "students" and "teachers or trainees" (non-student J status) are different, so it's more complicated than counting the number of years if you've been on non-student J status in the past.)
But if you have never been on F or J status before the current F1 program, and you've been in this F1 program for any part of less than 5 previous calendar years (remember that any part of a calendar year counts, so even if you arrived on F1 on December 31, that counts as "any part of" 1 year), then your time on F1 status this year should be as an exempt individual (exempt from the Substantial Presence Test), which should (unless you change to another status for most of the year) mean you don't pass the Substantial Presence Test this year, and thus be a nonresident alien this year. You don't get to "choose" not to be an exempt individual if you are in the first 5 calendar years.
Now there are some cases where someone who would normally be a nonresident alien can be treated as a resident, including the "Nonresident Spouse Treated as Resident" (one spouse resident/citizen and one spouse nonresident at end of year) or the "Choosing Resident Alien Status" (both spouses resident/citizen at end of year) elections, both of which would treat you as a resident alien for the whole year. Tax treaties can also be used to override the determination of residency, although I think that those usually only deal with when multiple countries claim you as resident, not when too few countries claim you as resident.
Any case that's an exception to the rule. This can happen because there are conflicting rules (and then one may take precedence over the other) or because there are international treaties that preempt general legislation.
For example, IRC 6013(g) election.
