Why is a human more closely related to a eucalypt than a bacterium?

Answer 1

A bacterium is a procaryote while animals and plants are eucaryotes. The basic difference is that eucaryotes consist of a great number of cells which can diversify in the many type of cells that exist in them: epithelial cells, nerve cells etc. Procaryotes don't have such ability.

Answer 2

Because bacteria are further down the evolutionary tree, (so to speak). Bacteria-like organisms split into the bacteria, animal and plant organisms - probably as a result of symbiotic relationships forming between different bacteria. Those that form symbiotic relationships with chlorophyll-like bacteria gained the ability to convert sunlight to energy, and became plant cells. Some became plant-like animal cells, such as the Euglena, These may then have formed a symbiotic relationship with mitochondria-like bacteria and gained the ability to form chemical energy from food, and became animal cells (amoeba etc).
Those that did not form symbiotic relationships remained bacterial.
This is of course a crude simplification. These splits would not have happened at the same time. This means that the bacteria are much older, in evolutionary terms, than plants and animals, including humans.
For a more detailed and excellent explanation, read Richard Dawkin's book "The Ancestor's Tale". It deals with exactly these issues.

Answer 3

The only reason I can think of is that a bacterium is a single-cell organism, while a eucalypt (and a human) are both organisms that reproduce, have multiple specialised cells, and pass on their DNA to offspring.