The idea is, they Oppose the Government but are Loyal in that they promise not to lead a mob with pitchforks to string them up; and they stand ready to provide an alternative.
Historically, the Opposition was the Loyal opposition not because it was against overthrowing the monarchy, but because in George III's day there were the "King's friends" and then there were the others, who most certainly did not want to be thought of as the "King's enemies". The term "Loyal Opposition" served to deflect the antagonism of the Crown to those who did not support its policies, whatever they happened to be. Later, when the Crown became a captive of whoever won the elections, the sense of the term shifted a bit.
But hang in there loyally opposing. Those who take pleasure in common sense and sound design support you.