“Anticipate no profit, provide all possible losses”. What is the rationale behind this accounting concept?

Conservatism

This concept emphasizes that profit should never be overstated or anticipated. Traditionally, accounting follows the rule "anticipate no profit and provide for all possible losses. For example, the closing stock is valued at cost price or market price, whichever is lower. The effect of the above is that in case market price has come down then provide for the 'anticipated loss' but if the market price has gone up then ignore the 'anticipated profits'. 

This Accounting Concept is called Prudence Concept. We should be conservative in recording the asset but should not underestimate the liabilities. This is to ensure that users of the financial statements are not misled.  

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The rationale behind this concept is that you should be Prudence when preparing financial Report such that Profit should not be realised until it is earned while all foreseen losses should be recognised. Always disclose the worst possible situation during Financial Reporting. 

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Conservatism  ( Accountant must choose the alternative that have least effect on income )             

This is Conservatism principle which is a needed treatment for Risk Management to avoid uncertainty.  You can not record the profit until realized and earned. 

Prudence  is one of the fundamental principles of Accounting. 

Do not overestimate the amount of revenues recognized or underestimate the amount of expenses.

You should also be conservative in recording the amount of assets, and not underestimate liabilities. The result should be conservatively-stated financial statements by which its users should not be misled.