Has anyone else ever noticed. On Facebook, and many other places, you have the option of liking your own posts.
That couldn’t be correct. Why would you like yourself?
And I have to tell you that I have been tempted too. So what would happen if I ever liked myself? 
I did once discover that, in their rather creepy words, “You cannot friend yourself”.
Because you do not lack self-esteem?
Some people say that it helps ensure the post shows up on your friends’ newsfeeds. As you may know, Facebook selectively fills the newsfeed with your friends’ posts. Not every status update is shown. One of the criteria Facebook uses is the number of likes a post has. By liking your own post, you add one more ‘like’, which may mean Facebook is more likely to put it in the newsfeed. I’ve just heard this anecdotally, so I’m not sure if it’s actually true or not.
I take photos of long distance running races, ski events, etc. After I post my photos I will often like photos of friends or people who did something special for the photo.
How did I know, without looking, who the OP is? 
Nothing much, but if you do it too frequently you could go blind.
One time I got confused and accidentally “liked” myself. I was embarrassed until I realized that you can “un-like” a post, including your own. In that vein, I’ve accidentally “un-liked” a post because I didn’t realize in time that I had already “liked” it. So, I had to “re-like” it. 