Can too much pride ruin a relationship?The attachment behaviour system is a big part of love and relationships. As children, we develop a bond to a select few figures (usually our parents) perceived to be bigger, wiser, stronger and kind. To these we turn for security and comfort when we need it. Attachment is a big part of our ability to love and long for someone. There is also a complementary caregiving behaviour system, which is why you find baby seals cute, crying babies uncomfortable, and feel good about being bigger, wiser, stronger and kind for someone.
In an adult romantic relationship, both our attachment and caregiving systems play important roles. As adults, we wish to turn to a partner in times of need rather than our parents, but now the relationship needs to be reciprocal, not hierarchical. In such relationships, we need to take turns being bigger, wiser, stronger and kind, while our partner is being small, frightened or sad. Love has two faces, the caregiver and the child, and we need to be able to express both for a relationship to be mutual, satisfying to both parties and stable over time. And then there needs to be some level of physical attraction and decent sex and a feeling of having about the same social status. It's not simple; relationships conform to the Anna Karenina principle.
Some children find that their parents react negatively to the expression of attachment needs. This will lead to what is termed avoidant attachment organisation, where the child minimizes the expression of needing the parent, while still maintaining an acceptable level of proximity. The child still forms a bond, but solves the problem by adapting it's way of expressing attachment needs. As an adult, these children will typically have problems expressing or even feeling a need for others when they are distressed, and typically fear rejection if they express their distress and need for comfort directly. Attachment avoidance can very well be thought of as a dimensional trait, rather than a discrete category of children.
What you are terming pride, I'd probably think of as attachment avoidance. At high levels, it will be both bothersome in general and lead to problems in relationships specifically.