In what sense are the US and China “rivals” today? When can “rivalry” be a good/bad thing?

The rivalry between the United States and China stems from the recent emergence of China as a great power on the world stage. Following the Cold War and the dissolution of the Soviet Union, the United States emerged as the sole superpower in the world. Superpower, in this context, means a nation or state with the ability to exert incredible levels of influence over the rest of the world, and project power, both hard (military) and soft (economic and cultural) around the world. The United States clearly fits this criteria, with its ability to wage wars simultaneously around the globe and its relatively strong control of the United Nations, as well as its leadership role among its allies in military organizations such as NATO and economic organizations such as G7. Recently, with developments leaning closer to nationalism rather than globalism, the United States has been said to be diminishing its role in soft power (though hard power, unarguably, is growing), though this tends to be greatly exaggerated, as the United States is still heavily invested in the world outside its borders.
China has been steadily growing in population, industrial output, technology, infrastructure, and military power for the past five decades. This has led to the state becoming a great power (level below a superpower, meaning they can project both hard and soft power globally, but would not be able to maintain the simultaneity of dealing with two or more separate global military situations, having less economic power than the superpowers, and are not as far-reaching in their capabilities as a superpower, though this line blurs as geopolitics develops today). China is steadily increasing its influence over the military and economic affairs of the East Asian region, which is seen as a threat to the United States considering that, in a zero-sum game, they are losing influence over such affairs in the region. China also is increasing its global investments, a role the United States both filled previously and currently fills, but again, in a zero-sum game, someone else gaining means one is losing influence. The United States invests globally, but China's recent developments have been in Africa and South America, two key emerging markets. Between its large military, strong economy, and increasing global hard and soft power, China is positioning to emerge as a second superpower, a scenario the United States has not been in since the dissolution of the Soviet Union.
This upsetting in the balance of power and restoration of a two-superpower world creates a rivalry between the United States and China. This is not the same, however, as a new Cold War. Though there is a great deal of espionage between the two nations, and noticeable proxy-"wars"(not shooting wars, but tense situations, namely Taiwan and the Koreas), the amount of trade and cultural exchange between the countries makes this situation markedly different from the Cold War. Rivalry can exist without a Cold War, however, and China's growing economy and influence certainly makes them a global rival to the United States. This rivalry, so long as it leads to good things such as a technological boon and rapid economic development (which is currently does, to a large extent), and not bad things such as the threat of war and poor/illegal trading practices (which it also currently does, considering the Koreas and Chinese labor and trade practices as well as American protectionism), can be a good thing. It is currently leaning more towards good than bad, but is a delicate balance that is easy to shake.

The sense that US and China are rivals stems in part from the growth in China's military, as it seeks to expand its power in Asia and across the globe. In addition, the US has been wary of Chinese trading practices, which they criticize for dumping products into the American market. China has become a major donor of aid to nations in Africa. While this aid may seem benevolent, some in the American press have criticized it as providing support for dictatorial regimes and for securing jobs for Chinese workers to build infrastructure projects abroad. In addition, some have criticized Chinese aid as entirely self-interested, allowing the Chinese to access raw materials abroad.
The US-China rivalry can lead to negative consequences, including military buildups and potential confrontations as China attempts to vie with the US for world power. However, the rivalry can also be positive, as it can put pressure on the United States to work with China in a strategic way. As China is a power that can no longer be ignored, the US needs to engage China in security and trade talks that are aimed at creating a more democratic country in China. Chinese aid abroad can also stimulate the United States to increase its own aid to developing nations in Africa and elsewhere.