Generally, that you would be less likely to reject it if X were true, and a couple of other ideas:
X is specific to your rejectiion—that is, that the truthfulness of X affects the probability of your rejection to a much larger degree than it affects the probability of other propositions that are conceptually distant.
The line of reasoning from X to reducing the probability of your rejection proceeds through certain types of connections, such as ones that are conceptually closer.
The effect of X is not too small, where “not to small” depends on how strongly the other factors apply.
(Human beings, of course, have lots of fuzzy concepts.)
Generally, that you would be less likely to reject it if X were true, and a couple of other ideas:
X is specific to your rejectiion—that is, that the truthfulness of X affects the probability of your rejection to a much larger degree than it affects the probability of other propositions that are conceptually distant.
The line of reasoning from X to reducing the probability of your rejection proceeds through certain types of connections, such as ones that are conceptually closer.
The effect of X is not too small, where “not to small” depends on how strongly the other factors apply.
(Human beings, of course, have lots of fuzzy concepts.)