לזכות הורי היקרים שיחיו

Why do we make Havdala when Shabbos ends and not when Shabbos comes in?? We say Kiddush to add Kedusha to an already holy day but we should also make Havdala as we do when Shabbos ends to separate between the holy and the mundane?!

The answer is that we don't have to make Havdala b/c the Havdala is automatic. The holiness "separates" between Shabbos and the weekday so we don't need a special tfillah. So when Shabbos ends the Kedusha leaves and thus the Havdala is an automatic. Why then do we have to say a special tfilla? Not only that but we would think that the central aspect of the liturgy is בין יום השביעי לששת ימי המעשה b/c that is when we are separating. But we see from the Gemara in Arvei Psachim [104] that we only have those words so that the bracha will be מעין החתימה [i.e. יום השביעי etc. is similar to the end המבדיל בין קודש לחול]. Otherwise, we wouldn't even separate between the seventh and six days. It is automatic. So what is Havdala all about??

Gan Eden. 

We started out pure. No evil. Then we sinned by ingesting the fruit of Good and Evil and the evil became mixed in with the good. In Mitzrayim we were taken out גוי מקרב גוי - we were swallowed up by the evil and were extracted. Pure good. Then this separation was completed at Sinai when פסקה זוהמתן - the impurity was removed [שבת קמ"ו]. But it came back after the חטא העגל.

When Shabbos exits there is a remnant of קדושה that remains with us. יציאת צדיק מן העיר עושה רושם!!! So we say Havdala so that the remaining קדושה shouldn't be contaminated by the mundane. המבדיל בין קודש לחלול בין אור לחושך בין ישראל לעמים!!! We want the קדושה to remain unsullied. When Shabbos comes in there is obviously no need for Havdala. It is an automatic. Just when it goes away we "separate" between the Kedusha that was etched on our soul and the חול that is to come. 

[עפ"י תורת מרן ראש הישיבה זצ"ל]