Why did te white men colonize the Igbo society in Things Fall Apart?
Short of being able to ask those specific white men themselves, you can look at a variety of historical reasons put forth for colonization:
One is the constant desire to expand, demonstrated throughout history by any nation or group of nations grown strong enough to do so. The desire for more land, more resources, more labor, etc., has driven countries to expand and colonize and continues to do so though it isn't always through direct colonization as it was in the case of Nigeria.
Another has been the drive of missionaries and others involved with religions to feel that they can help to "save" ignorant or backwards people from their wrong traditions and that drove some of the people who went to Africa, they felt they were spreading the gospel which would help to save the souls of all these people.