Good question.
First, here is an animated illustration of how the mtDNA currently suggests the migrations which populated the earth with modern humans occurred. Remember, at the time period this starts (150,000 years ago), Homo erectus had already been in Africa, Asia (including SE Asia), and Europe.
A second graphic follows:
Source: http://wwwrses.anu.edu.au/environment/eePages/eeDating/HumanEvol_info.html
If you will note in this chart, there were times when several different critters existed. In all cases, only one species, leading to modern humans, survived.
There is still argument over the "out of Africa" vs. the "multi-region" approach. This is essentially over how much influence on modern humans the earlier folks had; did the out of Africa migration shown in the Oppenheimer illustration (link, above) replace all earlier folks, or was there some interbreeding?
So, to answer your question, "why did we all evolve into the same species?" It looks like that the evolution of modern humans occurred in one place (Africa) and spread out from there.