Answer: The reason why an evolutionary diagram looks more like a bush than a straight line is the development of new species.
To be more clear - initially we can have one species, and that species will over time start to live in multiple different environments. As the species starts to adapt to the new environment, its appearance and genetics are gradually changing in order for it to have more advantageous traits to survive in the environment. As the time passes, the changes that will emerge in some members will create a new species, and that process will constantly go on, until extinction that is. So we have one species that is an ancestor of multiple new species, thus the family tree, or rather evolutionary diagram, starts to branch out, and as the time passes, it will branch out more and more and take a bush-like looks.