Immediately upon reading your post I thought of Garrison Keilor's fictional town of Lake Wobegon where all the women are strong, the men are good looking, and the children are above average. Doubt if it has much to do with why people play chess though; most of us are just plain addicted.
Why everyone thinks he/she is smarter?

Hey; that's where I live. Lake Wobegon. Love that NPR, Click & Clack, All Things Considered. One time he said, "The folks are going away for the weekend. Keep an eye on the Dog. He's got that look in his eye again".

People tend to overvalue themselves.
Since most people are average, they tend to think of themselves as a little better than average.

From my past experiences dealing with people, I came to a conclusion that every person regardless of age, education, etc thinks that he/she is smarter than the average joe.( me too)
Why do we think like that?
I guess, one of the reasons so many people want to play chess is to show that they are smarter?I
I think the reason is low confidence. if people had a high self confidence they wouldn't have to compare themself with others.
however having said that I guess it is human to compete with others
the answer isn't clear.
don't put too much into my answer I am just playing pocket psychologist.

You know, I can't remember ever thinking that I'm smarter than any one person, let alone "the average" person? I've always thought either that people are informed or not about a certain subject. Or, that they are purposely refusing to learn about a specific subject. But I've always thought that anyone can find out what I find out, so it really doesn't make sense to me that people think they are "smarter" or more "intelligent" than other people.

I worked at Walmart for a few years. I don't think I'm smarter than the average Joe, I know it to be so. I have witnessed the empirical proof of this again and again!

Try googling the term "Dunning Kruger Effect," and you will find a satisfactory explanation.
people that suffer from Dunner Kruger Effect makes it hard for others to compete for a job. even if they are just out of school they set the checkmark in expert in all experties.
thereas people with more realistic view would say they have a lot to learn and do not consider them experts.¨
guess who will come to job interviews.

I think it makes sense since wouldn`t anyone imagine that they are right.
If one thinks they are wrong then they woudn`t think it in the first place.

Opinion kinda bewilders me.
For example if someone has an opinion blah blah blah or whatever
the blah blah blah may not make any sense but apparently that is how opinions go so its not supposed to make sense since it is an opinion.
So it seems like maybe opinion isn`t supposed to make sense.
So if opinion doesn`t make sense how can it even be a word.
Don`t all words make sense?

Is it possible for someone to have the opinion that 1 + 1 = 2
or can this not possibly be an opinion since its just a fact?

Is it possible for someone to have the opinion that 1 + 1 = 2
or can this not possibly be an opinion since its just a fact?
you can also have an opinion that 2 +2=5 and be right.
if you have one worker and he can produce 2 pieces
and another worker can also produce 2 pieces
but if they work together they produce 5 pieces.
it is all a matter of how you explain it.
http://en.wikipedia.org/wiki/Synergy

It stands to reason that EVERYONE feels smarter than the average bear.
Indeed, Yogi Bear felt the same way.

an example that people think they are smart is the following facebook hype
TH15 M3554G3
53RV35 TO PR0V3 H0W 0UR M1ND5 C4N D0 4M4Z1NG TH1NG5! 1MPR3551V3 TH1NG5! 1N TH3
B3G1NN1NG 1T WA5 H4RD BUT NOW, ON TH15 LIN3 YOUR M1ND 1S R34D1NG 1T
4UT0M4T1C4LLY W1TH OUT 3V3N TH1NK1NG 4B0UT 1T, B3 PROUD! 0NLY C34RT41N P30PL3
C4N R3AD TH15. R3 P05T 1F U C4N
everyone is able to read it, nothing smart about it, but people hit the share button.
but people like the fact that only "certain people" can read this.
because they are among that group that can. Everyone is however.
From my past experiences dealing with people, I came to a conclusion that every person regardless of age, education, etc thinks that he/she is smarter than the average joe.( me too
)
Why do we think like that?
I guess, one of the reasons so many people want to play chess is to show that they are smarter?