This is Zim and Liz as Enemies

In many ways Liz hates Zim and often get into fatal fights and quarrels, mostly because Liz and Zim don't have a lot in common. Liz is an Irken who is naturally more like a human female, while all Zim cares about is trying to be 'human' and obessesses over ruling the Earth. Another reason why Liz and Zim don't like each other, is because that Liz and Zim are compeating for the same planet, Liz, knowing she was banished to Earth, is trying to impress the Tallest, while Zim, not knowing he is in exile, believes that conquering Earth is his mission.