It's always a bit awkward to say farewell to a friend or acquaintence for the last time. It's not really the farewell itself that's awkward - that can be kind of refreshing. During a friendship or acquantenceship, it's not really appropriate to acknowledge it as such, and so whatever's there just hangs in the air around how the people relate. People have emotional reactions (warm fuzzies, longing, irritation, fascination, etc) to each other, there is some status between them (friends make plans to hang out with each other, friendly acquaintences might hang out if they happen to spot each other while already doing an activity, etc), styles of interactions, etc. All of these things are kind of fuzzy, in flux, and potentially changed unless they're nailed down in some way - "who is kin" is relatively permanent (even if theoretically mutable, e.g. I no longer consider my father kin, while people who have been adopted into the family might become kin), "dating" has all of its own content, etc. When one says farewell, one packages the space someone took in one's head for storage and begins to step away from it, and so the normal tensions and status of how the people relate both become much more visible and it becomes kosher to express more of that openly. Sometimes this can be very uncomfortable, but only for a moment and still preferable to leaving things unsaid (e.g. "I've always hoped we would've been closer", "You irritate me to no end with your ideas about X", "I know you've never been comfortable around me and I regret the causes", "You've helped me with X so much and I regret I've not been able to help you with Y"). I've had things like these waiting for the post-mortem with many people, maybe saying about half of them - sometimes the right moment never appeared, sometimes I chicked out, and sometimes I realised that there was a lot more on my side of things than there ever was on the other, enoughso that expressing it really would just complicate someone's life. More than once I've told someone I felt something for them and I really wished (they had felt the same way/had been single sometime at the same time I was/they had broken from christianity a bit earlier/etc). For the things that are said, it can feel good to finally have unimpeded airflow between two people.
So it's not that final expression that's so awkward and regrettable, it's really more the bumping-into-them-a-bit-before-the-last-t