The creator of Tomcat ,James D Davidson , had initially hoped that the project would become open sourced and, since most open source projects had O"Reilly books associated with them featuring an animal on the cover, he wanted to name the project after an animal.He came up with Tomcat since he reasoned the animal represented something that could manage for itself without help of others ( are cats really of this nature !!!!). His wish to see an animal cover eventually came true when O'Reilly published their Tomcat book with a tomcat on the cover !
And ANT was there to build tomcat ! this Java-based build tool was developed as a side-effect of the creation of Tomcat as an open source project. According to Ant's original author, James D. Davidson, the name is an acronym for "Another Neat Tool".
Later explanations go along the lines of "ants do an extremely good job at building things", or "ants are very small and can carry a weight dozens of times their own" - describing what Ant is intended to be. Another resemblance with the animal world !