The positive aspects of the Columbian Exchange did not outweigh the negative consequences brought about through the conquest of the indigenous peoples of the New World. In the early contacts between European colonists and the tribes of the New World, the Native Americans generally fared much worse than the colonists.
In the Columbian Exchange, the colonists and the Native Americans exchanged food, livestock, and culture, with the intended result being the mutual benefit of both parties. Europeans brought gunpowder, the horse, and the Catholic Church to the New World, whereas the Native Americans brought new foods, new forms of game, and tobacco into the European realm of experience. Both the Europeans and the Native Americans benefited from the experience, though gunpowder and tobacco proved to have as many negative aspects as positive ones.
The truly negative aspects of the Columbian Exchange lay not in what was intentionally exchanged, but what also came about as a side-effect. The most devastating effect of the Columbian Exchange was the introduction of unknown diseases, especially smallpox, into the Native American populations. Because they had not had any experience with these diseases, Native Americans had no means with which to fight them. The result was the decimation of certain Native American populations.
Another negative side-effect derives from how new ideas and products were introduced to the Native Americans. When the Spaniards came to the New World, they imposed the Catholic Church on the indigenous peoples, feeling it was the only means by which to "civilize" them. This attitude toward the indigenous people contributed to the destruction of indigenous cultures. The Spaniards perceived Aztec rituals and practices as barbaric, so they imposed their culture on the Aztecs, killing Montezuma and destroying Tenochtitlan, only to build a new city on its ruins.
Ultimately, it is not what Europeans sought to exchange with the Native Americans that contributed to the negative aspects associated with the Columbian Exchange. It is what their unintended consequences and the means by which they interacted with the indigenous peoples that made the negatives aspects outweigh the positive aspects.