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The SEC has a rule that restricts the definition of an accredited investor to a person who has income in excess of $200,000.

(6) Any natural person who had an individual income in excess of $200,000 in each of the two most recent years or joint income with that person's spouse in excess of $300,000 in each of those years and has a reasonable expectation of reaching the same income level in the current year;

Title 17 → Chapter II → Part 230 → §230.501

How was this number decided, and what is the reasoning behind this decision?

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It's essentially a legally enshrined incentive for high net worth investors to supply capital, which is consistent with the other entities that qualify in § 230.501. It tends to come with increased access to riskier offerings, where the risk ensues from exempted registration.

While nominal dollar thresholds typically get eroded away by inflation, they needed a line in the sand to represent financial sophistication.

Speculation: I suspect the initial number was a ballpark attempt to approximate the point at which individuals (at that time) tended to be involved in more complex projects (e.g. certain hedges and ventures).

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put in the vernacular, an "accredited investor" is a so-called "sophisticated" investor who does not need to be protected from their own stupidity or from rapacious consultants who prey on passive market participants (i.e. 401(k) fundies.)

The number chosen IS essentially arbitrary. It's essentially 5x the median US income.

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