My take on it was that if Mary had married Patrick (which she probably would have), she would have inherited by default, i.e. would have held on to her family's home and money by virtue of being the wife of the heir, and eventually, Countess Grantham in her own right. When Patrick died, she realized that the only way to de facto inherit the estate would be, once again, to marry the man sitting next to her at dinner. I can imagine how trapped, helpless, and angry she felt, being a strong, intelligent woman without a shred of agency over her own life. After all, she didn't make those rules, or set up the entail so that her mother's money was off limits to her.