OP, sorry to hear about your story. IMO, you did not do anything wrong. It wasn't unreasonable for you to ask about other options when you landed in ORD. It was also reasonable for you to expect UA to honor the F booking that was made for you in DAY.

UA, on the other hand, showed its true colors. Even though, it is true, that policy states that you were supposed to be accommodated in Y, it doesn't mean that you could not be accommodated in F. And the fact that you were 1) downgraded and 2) also moved to a later flight without first informing you was reflective of an overall scourge of antagonism toward customers that has infected UA. (On the UA board here at FT, you will find plenty other stories of UA's underhanded attitudes toward customers, like UA misquoting upgrade fares and then later charging the credit card for the fare difference--without informing the passenger first.)

UA can claim that it is not doing anything illegal, which in general is true. But there are other airlines out there that still respect decorum and a certain level of decency toward their customers, instead of thinking that their customers are trying to take advantage of them.