Rational Expectations in the financial markets is an hypothesis created in order to explain / justify why the market is the only efficient means of allocation of resources to it's best use.

Rational in the sense defined by the hypothesis means that all currently available information is used by the market's agents to make decisions about resource allocations at that point in time.... i.e. investors of capital into the markets, and the market's clearing ability efficiently allocates capital for it's best use.

Now consider the "all currently available information" dependance.   This is information that investors acquire from business & market research, current events, and investor knowledge of business's and technical or financial conditions which will have an effect on those business's and their endeavors.   Using that information the hypothesis asserts that it's used rationally by the market's agents to make their decisions on allocations of said capital.  

But the key to the assertion is that market agents use of the composite market's behavior at the time is also used as information.. part  of the "all available information" assumption. 

What this means is that the independent assessments aren't independent at all... since they necessarily include information supplied by the composite market. 

To explain why this is proof of negation of rational market hypothesis, assume for a moment that each agent's independent assessment based on all the available information is not publicly available via the visible market.  Assume each agent sends their assessment (capital allocation... buy, sell, put, or call) for the entities in the market to a central but not visible repository.  Thus no participant knows what the composite of all other participants are doing in the market... truly independent assessments are being accumulated in the repository.   

Now consider how a single agent, on being made privilege to what all other participants are doing in the composite, will respond on seeing the composite.  There are only two possible responses --- 1) make no changes to the assessment they already made: 2) modify his assessment based on what they see in the decisions having been made by all the other participants. 

Understanding that the agent has no clue as to what reasons were used by the composite market assessments, they must make an assumption --- either the composite market has more information, or more reliable than the single agent has obtained, or they do not.  ... i.e. the single agent will either adjust their own assessment based on their own assumption of what the composite market knows they the single agent doesn't, or they will not be influenced by the composite.

If the single agent decides that the composite market has more or better information then they are assuming this is the reason why the composite market's assessment isn't the same has their own, but in fact they have no rational reason to make that assumption... since it is pure assumption... with no basis or foundation underpinning it.. .it's a pure WAG.. a "belief" with no objective or rational foundation. 

When the single agent assumes that the composite market's response is based on better or more information than they have then they will modify / adjust their own previously independent assessment to maximize their own beneficial gain (loss reduction) using the information supplied by the response of the composite market... which is to say they will decide with no rational basis to change their own assessment by pure assumption (WAG) that the composite market's behavior is based on information more informed than their own.

Now extend the single agent's privilege of seeing the composite market's behavior to all other agents simultaneously.  Thus the composite market agents are all adjusting their own assessments by using information from the composite market that purely assumes all other players in the market as a composite know something more than they themselves know.

This is the anti-thesis of rational decision making... it's a form of crowd / group response.  If one person suddenly runs screaming from the crowd, another will be stimulated to follow and only wonder why later... better safe than sorry so to speak.  With two running and screaming from the crowd, sure as shit four more will follow suit, etc. until the crowd is all following the original screamer ... nobody in the crowd having the slightest clue as to why the 1st person ran --- although there will be a plethora of reasons provided to rationalize the otherwise irrational response.

Therefore, since all market agents are using irrational reasons for adjusting their own independent assessments based on what the rest of the market in composite is doing, and they are all doing the same, then they are all, in the composite, ...  basing their market assessments and thus decisions on irrational foundation.   This is not a rational market behavior by any definition.

And there's actually an entire brand of market investment strategy dedicated to the fact that market decisions are based on no rational foundation what-so-ever... it's called 'technical analysis".   Technical analysis uses the composite market's response behaviors to decide whether to buy, sell, or hold in a given or group of investment entities at any given moment in time.  Market price patterns such as Head and Shoulders, and many, many other patterns, which occur over the course of a few trading minutes, or hours, or days, or weeks/months are used to assess the composite behavior of the market that has nothing what-so-ever to do with any knowledge of financial import at all.. simply a crowd behavior decision making method. 

Computer algorithms operating over nano-seconds of time are making buy and sell decisions at that rate .. when in fact there is no new relevant information available to the computer's decision making algorithm at all... simply using the composite market's behavior... basing decisions on what everybody else is doing... though without a clue as to why everybody else is doing whatever it is they'are doing.  The computer trading algorithm's are in fact agents that make no assessment related to the efficient and best use of capital in the composite... they use on financial information, no new business information, no information based on outside events and influences... rather the computer agent's decision is based solely on how all other agents are acting without any information as to why they are acting as they are.  It's the ultimate in irrational expectations.