Why did they pick 2200 to be a chessmaster?

You may become a chess master, but it would serve you better in life if you became a master of civility and humility.  Try working on that.

Arpad Elo devised the rating system for FIDE. In his testing, masters nearly always showed results at or above 2200. But that wasn't set by him; it was set by the national federations who used his system or a similar scale, like USCF. FIDE set the FIDE Master title at over 2300. IM & GM titles didn't have rating requirements until years later - it was based on your score against IMs & GMs in tournaments (what we now call a "norm"); the rating limit was put in later.

 Sounds like it is just one of those things that evolved.  I know that the USCF has periodically made adjustments to the rating formula.  Several years ago, my rating suddenly increased over 100 points without my having played a rated game.  I was told that it was the result of the USCF's having modified the rating formula to make the distribution curve more bell shaped.

Here's an excerpt that I came across a few years ago.  I don't have the link to the article.

The United States Chess Federation’s Elo rating system assigns to every tournament chess
player a numerical rating based on his or her past performance in USCF rated tournaments.
A rating is a number between 0 and 3000, which estimates the player’s chess ability. The Elo
system took the number 2000 as the upper level for the strong amateur or club player and
arranged the other categories above and below, as shown in the table below.

As I recall, when the Elo system was unveiled in the pages of Chess Review in the form of a ratings list of best US players, 2300 was master category. 2700 was GM.

Shortly afterwards, the catagories were dropped 100 ponts.

Now master was 2200.

Also a presupposition of the sytem was that an equal score in the US Open was what a 2000 would be achieving.

Actually you are wrong: You have to remember that at least for the USCF there is a 200 pt spread between classes. Thus 1400 - 1599 = Class C; 1600 - 1799 = Class B; 1800 - 1999 = Class A; 2000 - 2199 = Expert; and TA DA 2200 + = Master. Now the awarding of titles is based upon acquiring a set of "Norms". It is possible to be a National Master at 2200 but NOT be a FIDE Master. Generally speaking if you are a National Master the probability that you will have achieved all the Norms necessary to become a FIDE IM will have been achieved by the time you reached 2300, and there are a number of IGM who have a rating less than 2700

Originally the rating system was based on an average of all chess players and used to create a central Bell Curve the tails would represent the top and bottom 1%t they divided  the bell into 200 point increments and marked from the Center. Originally the AVERAGE USCF rating when I jointed was a Class "C" rating of about 1450.  Your PROVISIONAL RATING was based on tournament performance starting at the AVERAGE rating of 1450. Roughly 50%  of players were rated higher than 1450, and 50% were rated below. It tends to follow a School Grading System A --> F, and if you remember school a grade of "C" is considered AVERAGE. Once you get to 2000 you are a recognized EXPERT, after that at 2200 Master. In this regards this follows the Trades practice: Apprentice, Expert, Master.  Notice I said 1450 USE to be considered the AVERAGE rating.  Then something happened. That something is called SCHOLASTIC CHESS. Since the OLD rating system which was used for rating ADULTS falls apart for rating children who probably should not be playing in tournaments USCF devised an Age Based rating system. Now ADULTS age 26+ are rated starting out not at 1450 but at 1300 -- Class "D". Many OLDER Adults are a bit pissed off that the USCF allows children -- many frequently being coached in school, and privately by Experts and Masters, being allowed to play in tournaments with Adults. A sore point of contention for older ADULTS is to have to play an 8 year old who can't go to the potty by him or herself. These coached kids then start grabbing rating points from uncoached Adults. A review of the USCF's membership shows that over 50% of the membership is 12 years of age or under. But the USCF's own data also shows that another thing happens once these kids start approaching High School age: They tend to drop out of playing chess -- other sports, study, social activity such as dating, etc. By the time these children reach the end of High School, less than 5% of that cohort is still playing chess. So what happens to all those rating points. They are lost!! The lost of rating points due to the attrition of scholastic players has been liken to a Giant Black Hole -- the rating points go in, but they don't come back out. In order to "Fix" the system the USCF occasionally tweaks the ratings of established players by adding points back to their ratings, adding the most points to the lower rating players and fewer points the highers the established rated player's rating is. 

At some point in the not too distant future the USCF is going to become essentially a Scholastic Chess Organization with an elite cadre of Class "A", Experts and Masters and above at one end and Scholastic players on the other. Classes D,C, and B which use to constitute the Core ADULT member ratings. The Average ADULT will simply no longer support the USCF. Many older ADULTS no longer feel they are wanted, but their MONEY $$$ is so the USCF can expand its SCHOLASTIC CHESS footprint. Simply put there are way too few ADULT ONLY tournaments. Since USCF has gone to an Age Based Rating system, that would be 26 + years old. 

If you were to ask me what is an AVERAGE rating is TODAY, I would not be able to tell you. For the Average ADULT *probably* 1350-1400 would be my guess.

the number? totally arbitrary, same way 2800's ish is world champions of today.

but 2200's is usually the start of 99th percentile on rating distribution, 2000 is about 95th percentile last time i checked. being a master being equal to top 1% of players makes perfect sense to me

just think about it: if it would be 2100 you would say "why not 2000 or 2200?"