Why is it important that the Creation process is divided into 6 "days", as opposed to "parts" or "stages" or even presented in simple succession without mentioning "units"?
Rav Hirsch explains the reason for the terms Day and Night in Bereishis 1:5
The translation given below is that of Rav Hirsch's grandson who translated Rav Hirsch's German translation into English in order to keep showing exactly what Rav Hirsch meant to say. Note how it differs from the chabad.org translation.
And God called to the light: Day! and to the darkness He called: Night! and it became evening and it became morning: one day.
Rav Hirsch explains that this is not just a period of time or the usage of the day and night caused by the rotation of the earth under the light of the sun, but the creation of separate phases of existence. Thus each of the days is an independent creation (יום אחד one day) leading up to the final unit of creation in which the complete creation begins functioning.
This cannot mean simply He gave the name, for the words light and day are by no means identical, but day is the measure of time in which light rules over the earth, and similarly darkness and night.
In any case where got does call something by a name it always expresses a mission, a calling for the one to be so called as Abraham, Israel etc.
"Hashem called to the light and appointed it to the tasks of the day, and Hashem called to the darkness and appointed it to the tasks of the night". He directed both to their separate provinces.
Because Hashem wanted to make a 7 day (meaning, 24 hour period) calendar for us to keep Shabbos, every 7, literal days, like it says "6 days you shall do your work and on the seventh day you shall rest, for in 6 days did Havaya, Elokaycha create the heavens and the earth and on the seventh day he rested", if the "days" meant some arbitrary number of stages, then we shouldn't keep shabbos every 6, literal, 24 hour days, we should only keep shabbos maybe once every 2.4 billion years, why not?