why did the struggle for independence loosen the bands of government everywhere as john adams remarks

what he meant was that by the USA revolting against their government they were sort of an inspiration to other people to revolt against their own governments.

The correct answer to this open question is the following.

John Adams is answering one the many letters his wife-Abigail Adams - had written to him. Adams referred to his quote that "independence loosen the bands of government everywhere" because in that time almost everyone was questioning the issue of liberty. All people were trying to be free - even the slaves were questioning the issue of slavery - and women also. Abigail had written a letter to her husband regarding the issue of women's legal protection in the Constitution.