An emotional barrier to faith isn't really like a question that I can just provide information to answer. It's something that has to be worked through. Just like in any other relationship, emotional barriers between a person and God have to be worked through one step at a time. But for some reason, God seems to use other believers to help in that process. Here are some things that I've noticed can be really important to helping others walk through this process.
Validate the person's feelings - You'll never get anywhere in any kind of relationship if you spend your time arguing that a person should not be feeling that way. Whatever the cause and however reasonable or unreasonable, justified or unjustified, a person's feelings are there and they have to be worked through rather than argued out of. The first step to working through an emotion seems to be acknowledging it's there and accepting it. And it's a lot easier to do those things if we have someone walking with us who can help us to see that the feelings are ok, but who also might gently ask us to consider where those emotions are coming from and what they really mean.
Challenge assumptions by asking questions - A lot of the barriers to faith that I've seen are actually barriers to perceptions about God that aren't accurate. For example, a person who believes that God is arbitrary and capricious and not inherently good might have a real barrier at an emotional level to putting faith in a God like that. But I don't believe that God is arbitrary and capricious, and the God that I have known and learned to love does not have those characteristics. So in a relationship with a person who believed that about God, I can tell stories of how I have encountered God in my own life, and I can invite a person to reconsider whether what they've heard about God and think is true about him is really true about him.
I can do that in a couple of different ways:
I can share how I've worked through those same questions about God in my own life. This is basically telling stories of what has happened to me--where did that question come from or when did it come up, the questions I asked of God, and how I came to a point of resolution or peace or relationship in the context of that question.
I can also introduce people to Jesus in a way that engages their emotions and encourages them to engage Jesus relationally. Again, I think that telling stories about Jesus is the most powerful way to do this because stories grip the attention and invite us to imagine and experience something in a way that we might not have been willing to before. This might be as simple as paraphrasing a story from the New Testament. It might also be using materials that others have created that focus on this. Over the last year or so I wrote seven stories of peoples' encounters with Jesus in the New Testament, and I included questions for discussion or reflection. They were meant to invite people to engage with Jesus with in an emotional and relational way.
One important thing to remember is that when Jesus told people stories to engage their emotions and invite reflection, he often didn't tell them the answer or impart his knowledge in a kind of lecture. He could tell a story and let it sit with people, and he trusted that the Holy Spirit was working and would illuminate truth in that person's heart. It's something like telling a fairy tale without having to add the moral of the story. When you leave the moral out, you invite a person to do the work of allowing the story to penetrate the heart. That's one of the reasons I think Jesus's parables were so powerful. It's easy to disregard another person's conclusion or moral as something that works for them. It's harder to ignore when a story gets inside you and rolls around in your head and your heart and begins to challenge your assumptions and your values and your choices.
What does it mean to engage with Jesus relationally (as opposed to intellectually)? How could you invite someone to do that? Do you have words to describe your relationship with Jesus in terms of relationship rather than belief system?