Imagine bitcoin worked using a PoS.  An early adopter had acquired 1M BTC at one time in the past but over time he lost/sold/spent/transferred them.   Today he has no bitcoins but the blockchain contains a history of a time when he did have 1M BTC.  If the amount of the stake being used is <1M BTC he could rewrite history not by using coins he has today (a real cost), not by buying millions of mining rigs (a real cost) but by using the history of the coins he once had (no cost).  He has absolutely nothing at risk and nothing to lose.   If he and potentially others decided to attack the network they would rewrite the blockchain starting from when they had a larger stake, creating a parallel history where they didn't lose/sell/spend/transfer the coins. 

They can attack the network based on what they had (but no longer do) in the past.  There is nothing at risk and no cost to the attack.  THAT is the PoS problem.