I wasn't aware the analysis estimated a player's strength.
How accurate is the chess analysis

No, the analysis itself is rated about 2000, I think
That's what I understood too and more powerful analyses comes with subscriptions.

I did a chess analysis today of my first game ever played on this site and it said I played at a strength of about a 2000 player rating. I don't believe it.
Wow, somebody sure is self-confident...

Not self-confident, he misunderstood it when it said that the strength of the computer analyzing his game was about 2000. If he was confident that he was so great at chess, then he wouldn't be questioning the accuracy of what he thought was the computer's estimation of his strength.
Or you were being sarcastic, and saying that he should have more confidence in himself. It's hard to tell over the internet.
I did a chess analysis today of my first game ever played on this site and it said I played at a strength of about a 2000 player rating. I don't believe it.