I don't have a whale moment, but my manatee moment gave me feelings that are probably similar to yours re: being incapable of feeling anything but respect and awe for the aquatic mammals we share the planet with.
In the late 80s my father took me snorkeling at the Crystal River Manatee Sanctuary[0]. We rowed our boat out into the river and anchored. I jumped in and immediately spotted an adult manatee and a calf. I've always assumed it was a mother and her calf.
Judging distance under water is difficult, but I'd put them at least 40 feet away in water that might have been 12 feet deep.
The mother put herself between me and the calf surprisingly quickly. Knowing the rules I didn't approach them. I just floated there watching.
After a few moments the calf poked its head around its mother and looked at me. It felt just like a curious child peeking from behind a parent's legs. I stayed still and just watched them (thankful my father made me wear the yellow Navy surplus horseshoe collar BC that had just enough air in it to keep me afloat without the need to tread water).
My father was still getting his SCUBA gear together and hadn't jumped in yet. I think I stuck my head up and told him they were there-- I can't remember for sure-- but I know he stayed in the boat for awhile leaving me alone with the two manatees.
As I watched over the next couple of minutes both mother and calf went up for air and moved closer to me. It seemed like they were grazing along the bottom in the plants. I didn't see them eat any of the plants, but it seemed like they were nosing around in them. I definitely got the "sea cow" comparison.
The mother got close enough for me to see ugly gashes in her back from being stuck by boat motors. They weren't bloody or raw-looking, but they did look deep and painful to have acquired. Her calf's back was smooth and a lighter color.
As they proceeded past me the calf turned, swam over its mother, and approached me. I was shocked at how fast it could reorient itself and move. Again, having been told the rules, I kept my hands close to my body and didn't move. The calf bumped into my legs and rubbed against my back as it swam past. It descended and circled back around under me and rejoined its mother. They continued swimming away from me, into the murkier deeper water and down into the sanctuary where we weren't permitted to follow.
The whole thing might have lasted 5 minutes, but it really stuck with me. The memory is surely tarnished and altered, having been recalled so many times, but I definitely got bumped by a curious manatee calf whose mother was wary but didn't flee.
[0] https://en.wikipedia.org/wiki/Crystal_River_National_Wildlif...