On social media, I notice that people deliberately omit the word ‘I.’ What might be behind that?

None of the answers satisfy me, though Logan R. Kearsley’s is by far the closest to satisfying me.

EDIT: Uri Granta’s answer satisfies me more than mine. Go read that.

There is a colloquial register in English, in which the first person subject is omitted routinely. It predates social media; see, for example the Beatles’ A Day in the Life. The bits Lennon wrote use the pronoun; the middle section McCartney wrote skips it:

Woke up, fell out of bed,
Dragged a comb across my head
Found my way downstairs and drank a cup,
And looking up I noticed I was late.
Found my coat and grabbed my hat
Made the bus in seconds flat
Found my way upstairs and had a smoke,
Somebody spoke and I went into a dream

But contra Logan, I don’t think this is just spoken English. I think this is a particular narrative register of spoken English—it’s a conventionalised way of telling stories, in a punchy way. I don’t think you’ll find it in different kinds of speech, such as say persuasive speech or instructional speech.