Why An Ark

Why the need for an ark? G-d could have saved Noach in any number of miraculous ways. 

There are several approaches to this question. A few of the approaches:

1. Rashi (7:14) says the point is the building of the ark so that people would ask and be told by Noach to repent. 

2. The Ramban says that G-d likes to minimize miracles and make events seem natural. Interestingly, the Ramban's reason for this idea is that humans must do their part, and Hashem completes the rest. This is a mussar idea that man must put in their full effort and ask Hashem to complete that which is beyond control. This is in contrast to the philosophical approach advanced by the Ralbag here in To'elet HaShevi'i, who emphasizes that Hashem only breaks natural law when absolutely necessary, because G-d wishes to uphold the perfect laws of nature which He designed. 

As mentioned on my father's blog 'Rogatchover on building the teivah: is the mitzvah the maaseh or the totza'ah?' the Rogatchover proves that Noach didn't have to build the teva himself from the fact that he got help, and אין שליחות לעכו" ם, it must be the point was just that the teva be built. We see from the Rogatchover that if the point is that the action is done, then one can perform the mitzvah through a gentile, and one does not need the parsha of shlichus. This yesod is also said by Rav Elchonon Betzah, siman 25, as to why one can fulfill the mitzvah of burial through gentiles. We can use the same idea to explain the opinion of the Magen Avraham (446:2) that one can fulfill the mitzvah of תשביתו שאור מבתיכם through a genile.  R' Akiva Eger asks אין שליות לעכו"ם?  According to this idea, the Magen Avraham holds that the mitzvah of תשביתו is to have the chametz removed (see Minchas Chinuch mitzvah 9), and for that one can fulfill the mitzvah even through the actions of a non-Jew.  

3. The ark was a miniature world. The world was created through kindness. That kindness was being obliterated by the חמס of the generation, and therefore they had to be destroyed. In order to keep the world going, Noach had to provide for the world around him to allow the world to continue to function (based upon Rav Dessler).  

4. Bereishis Rabbah 31:9: "Kanim ta'aseh es haTeivah" – like a bird's nest that purifies a metzora, so too the ark was a spiritual purification for Noach. How? Perhaps Noach was a צדיק בדורותיו ולא בדורו של אברהם because he was dragged down by his surrounding society. Instead of maxing out on his potential, he settled for being better than the rest. The teva was to teach Noach that one has to view themselves as their own little bubble and not be influenced by society at large. 

5. The Baal Shem Tov teaches that the word תיבה can also mean word. To escape the torrential מים רבים surrounding us, one must be able to retreat into the words of Torah and tefillah. The Kedushas Levi notes the dimensions of the teva, 300 = ש, 50 = נ, 30 = ל spell לשן tongue. The teva teaches us how to measure our speech properly. The Noam Elimelech adds צהר תעשה לתיבה, if speaking, one should ensure their words shine like the light from the ark.