Because the illegitimate tyrannical monarch King George III was oppressing the colonies.
So? You're supposed to be a good little royalist. It's his divine right to tyrant his colonies.
If you're going to royally get rid of him you do it George RR Martin style. Plots, murders and some other toff who's got a claim to the throne because his daddy was related to someone important. You certainly don't start a rebellion that seeks to defy the divine right of kings.
Or you can try being consistent and allow the British people to have their freedom to vote and elect people to run things the way they want, given that you're all for those colonials getting a slice of theirs.