Because the incentive is what drives change. You're not going to convince America or Western Europe to live strict vegan lifestyles if they are adverse to it. Further, as the poor people grow wealthier, they begin to eat more meat unless they have a religious reason (I.e. an incentive) to do so.
Converting to a vegan diet alone won't stop human driven climate change. Therefore, the prospect of climate change won't be enough to convince people to give up meat en masse. That drum has been banged on enough for long enough for that to be obvious.
It's not even just America or Western Europe. As soon as I saw the OP about switching to total veganism, my first thought was about e.g. the Arabian Peninsula where meat is central to every meal, and indeed going without meat is seen as the behavior of adherents of foreign religions. Anyone familiar with that part of the world knows that any fad of societal veganism would take decades to arise, longer than the time we have to tackle climate change.