Why were you instructed to keep swirling the erlenmeyer flask?

You are instructed to keep swirling the Erlenmeyer flask to make sure that the solutions already inside the flask would stay mixed and not separate into different layers.

You are instructed to keep swirling the Erlenmeyer flask to mix the reactants. Assuming you have been doing a titration experiment and I am doing your homework it is so as you add the acid/alkali you can accurately close the biuret when the indicator changes color. Therefore, to make sure that the solutions already inside the flask would stay mixed and not separate into different layers. It is ideal to keep swirling the Erlenmeyer flask so the solution added, later on, will mix well with the rest already inside the flask.

They are called independent