What this means is that the creature thinks that his creator, Victor Frankenstein, owes him kindness, mercy, and affection.
The creature is of the opinion that Frankenstein owes him a debt. Frankenstein created him, just as he would've created a son or a daughter, albeit in less unusual circumstances. The creature therefore feels entitled to the same kind of treatment that a parent would lavish upon their child. And yet Frankenstein has rejected his creation, making the creature feel decidedly unloved and unwanted.
In saying that Frankenstein is equitable to everyone else, the creature is drawing attention to Victor's decent treatment of those around him. That being the case, he thinks it deeply unfair that Victor should trample upon him alone, the very creature that he has created and to whom, according to the monster, he owes justice, clemency, and affection.
In short, the monster in the above excerpt is asking for equal treatment from his creator. But as he realizes he's not going to receive it, he goes on to demand instead that Frankenstein make him a bride. He hopes that this creature will provide him with the kind of companionship that Victor refuses to give.