The study of decision-making tells us that we like to think that we make our decisions based on facts and reason, when in reality we make decisions at the emotional level and then post-rationalize them with facts & figures that fit our narrative
People buy into things because it makes them feel safe, secure or increases their status. I deeply believe that if you want to sell your ideas, you have to hit people at their core and make the alternative appear so unappealing that they have no choice but to side with you.
You can think of the hierarchy of needs in the decision-making process as something akin to Maslow's pyramid of needs, which many of us are familiar with. At the bottom, people will make decisions that are the most likely to help them survive (fear-based) and at the top, there are people who make decisions because they are self-actualized and want to leave a legacy (ego-based). Evolutionary psychology helps us understand these behaviours better.
Your job as a service provider is to identify who your stakeholders are and speak to them on an emotional level, by making the alternative so unappealing that they'll feel they have no choice but to hire you to design their next building.