The world needs engineering graduates that can develop solutions that extend beyond the purely technical aspects of solving a challenge or problem. Engineering leadership education provides a strong mechanism for engineering educators to develop an engineering mindset that embraces the development of a depth and breadth of nontechnical skills as being a key element of engineering education. This can lead to engineering graduates that are comfortable working across disciplines and contribute broadly to creating positive solutions to large and complex sociotechnical challenges. Notwithstanding, developing and integrating non-technical skills associated with leadership, such as social intelligence, developing vision and working in interdisciplinary teams beyond engineering is a systemic challenge. In this paper, the authors propose that a major barrier to systemic change toward enhanced non-technical skill development is the existing culture in the engineering education institutional environment. This paper is based on our personal experience in both advocating and implementing a broader mindset in the engineering curriculum. We begin by exploring the tensions in the culture of engineering education through the lens of Hofstede's cultural dimensions. We then follow with a discussion of the co-contraries that exist in engineering education within the bounds of these cultural dimensions. We conclude with thoughts on how concepts of engineering leadership could be leveraged to influence culture change that can positively influence the curricular aspects of engineering programs, as well as within the institutional environment. The work in this paper provides a baseline for discussion on how engineering educators can work to bridge the culture gap that arises from the systemic cultural tensions.