Hey @Kyle,
That is a great idea to learn more about your contacts! Most importantly, it certainly is possible!
@julie.accardo gave some great options by using the default functionality of Klaviyo to gather this information; but you can also accomplish your goal and suggestion by utilizing and Custom Coding your own Unsubscribe/Manage Preference page using HTML/CSS. As part of your custom Unsubscribe page, you can include this field of “Please tell us why you no longer wish to receive emails from us” and their selection of reasons as to why they are unsubscribing; that when selecting one of these options and unsubscribing would tag these contacts with a Custom Profile Property.
With these customers tagged with this custom profile property such as “Unsubscribe Reason”, you can then create a segment of these users who has this profile property using the rule of “Properties about someone, Unsubscribe Reason (or whatever the name if your custom profile property being passed is) is Set” and Export this Segment while including this profile property field as part of the export; would allow you to analyze these reasons as to why your contacts decided to unsubscribe via a .CSV.
-David