A couple of reasons, in this case for a Postgres instance that has 2TB of data.

1) price: you’ll easily spend $$$$$$ on RDS. If you host it on something equivalent with native SSD you’re looking at $800 a month with better performance

2) performance. It’s way faster and you can tune your indices, create views and make it fast and efficient in a predictable way.

3) if you want to, you can easily migrate to a different service. We did just that two months ago, from google cloud to AWS. It gives us vendor independence.