Its about two stepsibling who fell in love with each other. But cannot say a word. Cuz they are brothers. She say that if they knew each other when they were little maybe they wouldn't have this fellings.
Three years late, but the more I come back to this story, the more I'm seeing the symbolism in it. There's a lot of references to 'time' and 'reincarnation' in the story. On the cover page, you can see wheels in the bottom right corner, which likely symbolize the wheels of time. You also have the butterfly in some of the pages, which symbolize death and reincarnation.
The title is also 'A Cat That Loved A Fish.' The 'fish,' we can assume, is that celacanth (misspelling of 'coelacanth'?), which was a prehistoric fish. Seeing how the MC said 'In order for people to just pass each other in the present, they have to have 3000 encounters in their previous lives,' I'm assuming that the title's deeper meaning is that their previous lives were the coelacanth fish and maybe some sort of prehistoric cat, and they fell in love with each other, but since they were different species, it didn't work out. And now, thousands of years and many reincarnations later, they meet once again, but they still cannot be together due to their parents being married and them becoming siblings. The love between the cat and the fish is parallel to the siblings' love. So it's like they were destined to be star-crossed lovers all this time.
Who said they can't marry. They are step siblings so they can, if they were half siblings they couldn't!

I like the name of this manhwa,it has a deep meaning :) and manhwa is good it would be nice if it has more :/