Everything on nostr is a note. There is no relational database behind the website that prevents me from liking my own post, therefore a note that says:

- I am a like

- I like note with ID: xxxx

- I was created on Monday 1st ...

Not only can you like your own note, you can even like it an unlimited number of times.

Clients often enforce rules to prevent such things so that it feels more like a "twitter" clone, but that's what clients do. They take a technology that is so vast it can do anything, and introduce rules to give it meaning for their specific use case.