@DavePhD already gave a good description of how to prepare the solutions.
Here are possible good reasons why the teacher doesn't like your original proposed method:
does not work in practice (unless you mean: prepare a bit more, and then pipette 5 equal amounts). But if you pipette, there is no reason not to pipette the amounts of stock solution that directly lead to the neeeded volume for the dilutions.
is no volumetric glassware, and in addition not the preferred glassware for mixing (though mixing with magnet stirrer is OK). Volumetric flasks are much better: you can close them and then thorough mixing is possible. If you don't have volumentric flasks, Erlenmeyers are better than beakers.
would it be easier to dilute them by half each time
That would lead to an exponential series of dilutions, like 1 mol/l, 0.1 mol/l, 0.01 mol/l etc. instead of the equispaced concentration series you describe. Also, serial dilution means that concentration errors build up: each dilution step adds error.
Ultimately I will need 200ml of each solution
With volumetric flasks, you can directly prepare 250 ml of each solution. Your proposed method would lead to varying volumes. It is unlikely that the proper volumes are available as volumetric flask.
Calculating the needed volumnes for the volumetric flask + pipetting stock solution or the graduated cylinder version is easy. A plausibility check of this can probably be done on the fly in the lab without calculator.
Calculating the needed additional volume for your method is somewhat more elaborate. This is of course a bad reason if it is only about laziness. But it is a good reason if it is about doing plausibility checks while doing lab work.
Last possible reason: working with volumetric flasks thorough mixing is easier and the volume is anyways more precise than with a graduated cylinder. (Far more precise if you are still learning the practical skills of lab work: with the graduated cylinder you neet to get both volumes right at the first attempt.
With a pipette getting the volume right is much easier. So only the flask volume needs to be right at the first attempt - and the flask has a neck that helps with precise volumina.)