This petition was rejected

The Government e-Petitions Team gave the following reason:

We can't accept petitions about appointments, which includes calling for Cabinet Ministers to be sacked.

In any case, as you might already know, the Prime Minister of the UK is not chosen by the UK Government or Parliament.

After a general election, the Queen decides who to invite to form a Government. In practice, this is usually the leader of the political party that wins the most seats in a general election. You can find out more about this here:
www.royal.uk/queen-and-government

If you're concerned about a particular policy or decision that's the responsibility of Government or Parliament, you could start a petition about that.