Where and when

The setting matters more than the wording. Disagreeing with somebody publicly, in front of people whose opinion they care about, converts a small point into a status problem — and they will then argue to avoid losing face rather than because they believe it.

Timing works the same way. Raise it before the decision rather than after, while it is still cheap for them to change. And if the moment is wrong — they are stressed, it is the wrong room — say you would like to come back to it, and then actually come back to it.