Why was aptitude removed in favor of apt-get?
Solution 1:
This has been covered in Bug #592336 on LaunchPad. However, in summary it was decided during the UDS-M (Ubuntu Developer Summit) that 2 additional MB could be gained on the limited LiveCD image if Tasksel and Aptitude were removed.
The initial reason why aptitude was included in ubuntu was that the desktop installer (ubiquity) depended on it, but now the desktop installer has been rewritten to not require it unless in particular cases, and hence it goes.
Since the installer no longer requires aptitude, having it installed dynamically when needed, rather than including it in the base image, won as the better course of action.
We could substantially reduce the size of the minimal seed by installing tasksel and aptitude dynamically, so that we don't end up with them on live-installed systems.
Both the spec and Ubuntu Wiki page for the Maverick Spring Cleaning state that removing this from base has a great benefit for the inital seed and base size.
Solution 2:
Colin Watson Explains the reasoning behind removing aptitude:
[...] aptitude has a different dependency resolver which handles things quite differently from apt-get, and the fact is that we simply do not routinely test that dependency resolver. [...].
The base system is constantly tight on space, and everyone wants a piece of that space. [...]
(my emphasis)
His full explaination can be found on Bug #592336.