My favourite colour is blue. If you has asked me what my favourite colour was when I was say, 4 years old, it's likely I would have said, ... "Because!". Kids are pretty blunt and uncomplicated like that. Cut to primary school and the same question will get a rationalised response. "Because it's red like a fire truck", or "Because princesses wear pink".
From an early age, part of development is learning to rationalise and justify, to explain why you have the opinion you do. Imagine if the answer to "what is your favourite colour?" was "Because I am guided by deep unconscious processes that I do not fully understand which make me spontaneously reply blue". So much easier just to say "Because!"
Now to the business context. Imagine you are trying to justify an investment but one of your stakeholders doesn't like what you're proposing. Why? "Costs excessive, no funds available, risk to customer retention, incompatible with brand values...." - all rational reasons that may be cited. But really, why? "Because!" Now that may be the real answer. Whilst the rational reasons have been stated, there's a strong possibility that you are actually dealing with something a little deeper - the gut reaction which in this case has worked against your project.
That's the trick our minds play on us. Whilst the stakeholder might truly believe the rational objections to your idea, the main issue is more likely to be with their gut.
In his book Blink, Malcolm Gladwell introduces the concept of thin slicing - "the ability of our unconscious to find patterns in situations and behaviour based on very narrow slices of experience" (p 23); of recognising patterns and making snap judgments. At an early age, I made a snap judgment that blue was my favourite colour, and throughout my life I have stuck to that. In everyday language we're talking about "a gut feel". Gladwell sets out to convince his readers of three things 1. that decisions made quickly can be every bit as good as decisions made cautiously and deliberately, 2. that when rapid cognition decisions go awry they do so for very specific reasons and 3. that snap decisions can be educated and controlled.
So back to your stakeholder who has made a snap judgment about your proposal. Look at it from their perspective - what patterns may they have seen that has set them against proceeding? Sure you can counter their rational concerns with facts and data, and you might even (begrudgingly) get the signature. But what's underneath the surface that might mean you have won over the head but not the heart?
Short of using techniques like the "5 why's" and metaphor elicitation (using visual imagery to draw out the unconscious), your best path is looking at change management tools to pitch your proposal to both the gut and rational levels. A great read on the subject is Switch: How to Change When Change is Hard by Dan and Chip Heath. In this book they use set out actions to 1. Direct the Rider (the rational brain), 2. Motivate the Elephant (the unconscious) and 3. Shape the Path.
Rest assured there are ways to both unpick the unconscious motivations and guide them to your end - the hard part is taking the time to consider the thin slice, to answer the "Because!", and to make sure that you can convince your stakeholder's gut that it's the right decision.