Rivalry between a rising power and an existing superpower is inevitable. How it gets resolved though is not certain.
China is on track to overtake the US economically in a decade or two (if you consider PPP adjusted GDP they've already surpassed us). That have implications in other areas too -- strategic, diplomatic, cultural, etc. How will the US respond to this? Will we simply let it happen or will we stop it and perhaps violently? What will it mean for our agendas in different areas since China and the US don't share the same goals in many areas. What's especially frightening to me is that Xi seems to advocate a view that China's rise is a return to a historical greatness and that China is destined to dominate -- similar in some sense to the old "manifest destiny" idea of the US. Xi's idea is now enshrined into the Chinese constitution along side Mao's ideas. My view is on this rather bleak but I think the US needs allies more than ever. Ironically I think two equally matched powers are more likely to come to a peaceful coexistence than if one side perceives the other to be weaker. Maybe a new cold (or cool-ish) war isn't so bad compared to a hot war.