"Nontransitive preferences" are when your preferences contradict each
other. For instance, if you prefer an apple to a banana, an orange to
an apple, and banana to an orange, you have nontransitive preferences.
An unscrupulous grocer could trade you an apple for a banana plus
$.05, an orange for an apple plus $.05, and a banana for an orange
plus $.05 and make $.15 from you without improving your situation in
any way.
For most purposes, nontransitive preferences are irrational. But
maybe this doesn't cover people's preference to exist. If you'll
indulge some ontological looseness for a moment, maybe it's entirely
reasonable for "nonexistent people" to have little or no preference to
exist, but for existing people to have a strong preference to continue
to exist.
One could say that what counts is state transitions rather than
states. That is, people prefer not to change state from existent to
nonexistent (or as we uneducated masses say, to "die") but have no
strong preference whether to change state from nonexistent to
existent.
I don't think this holds up well. Most people would prefer that, if
they die on the operating table, they should be brought back to life
if possible. There are exceptions but seem mostly due to poor quality
of life due to poor health.
One might counter by claiming that a person who dies on the operating
table doesn't really cease to exist, since medicine can resuscitate
him. I don't think that rebuttal works. Even if a person could
entirely cease to exist and be brought back - think Star Trek
transporters - I expect people would again prefer re-existing.
So we really are talking about state preferences, not transition
preferences.