Diamond does not talk about the motivations of the Europeans in any depth because they are irrelevant to his thesis. Let us look first at what historians say the Europeans’ motives were, and then discuss why they were not relevant to Diamond.
Historians typically say that the Europeans went out and colonized territories for three reasons. These reasons are summarized as “God, gold, and glory.” Europeans colonized partly because they thought Christianity was the one true religion and wanted to allow non-Europeans to be saved. They colonized in part because they wanted wealth (both for the individuals and the countries doing the colonizing). They colonized in part because they wanted prestige. Again, this motivated both people and countries.
But none of this matters to Diamond. He wants to know why it was possible for the Europeans to colonize, not why they wanted to do so. His thesis is that the Europeans were able to dominate the world because they were lucky in terms of their geography. They lived on a land mass that was lucky enough to have the conditions for agriculture to arise early on and then to spread. This gave them a more powerful civilization than that of the natives of continents other than Eurasia.
This thesis is not affected in any way by the motivations that the Europeans had. The Europeans could have been motivated to conquer, but it would have been unimportant unless they were also able to do so. Diamond, therefore, focuses only on the factors that made the Europeans able to colonize, not those that made them wish to do so.