A classic example is saying that things are fine when it really isn’t true. Whether you rationalize by thinking saying fine will "avoid conflict" (it doesn’t in the long run) or you think you're just "being polite", that small dishonesty grows over time and erodes intimacy. It demonstrates a lack of trust, whether in the other person’s ability to handle your truth, or in your own ability to manage your feelings, or both. Politeness is fabulous at the grocery store, or with acquaintances and casual friends, but if you truly want an intimate relationship, it’s important to be open and honest with each other. You could say “I’m not sure how I feel, let’s talk later”, or “I’m feeling unsettled but don’t want to talk about it yet” or even "I’d like to say I’m fine but I think that might not be true.” Taking a time out when feelings run strong is helpful, but please let your partner know that you will be back to resolve the conflict.
Sometimes people are ashamed of something in their past or something they are currently doing and assume that if their partner knew, all would be lost. So they keep it secret, and the feelings of fear (the other might find out), guilt and shame (self judgement) create little breakages in intimacy. Over time, these little breaks can widen into canyons. Sometimes people have a habit or a history they want to keep secret for fear of the other becoming angry or judging them if they knew. Perhaps it is a hidden friendship, drinking too much, gambling, a past lover, a secret lover, a purchase, a crime. It doesn’t really matter what the secret is; it is the keeping of the secret that causes distance in relationship.
A third pattern is neglecting to make choices that take into account what is best for the relationship and instead enacting your sense of entitlement of what is best for you as an individual, regardless of the impact on the other. This is a tricky arena because it is important to take care of ourselves ("put your own oxygen mask on first") and at the same time we need to take care of and nourish our relationship. We need to find a way to balance individual / relationship the same way we need to balance individual / community in light of social responsibility. Communication and negotiation skills are helpful here, as avoiding dealing with issues does not make them go away.
Allowing another to know you deeply can feel risky. It can also be absolutely amazing. And, as with most things, it is a choice that you make on a daily basis. Instead of simply repeating old familiar habits and behaviors, let your choices be more conscious with the intention of creating of the kind of relationship you want.