Let's start with the foundation of human rights: the proposition that all men are Created equal.
This is not what reason tells us. Reason shows that some folk are smarter, better looking, richer, and made unequal by any and every measure imaginable. Yet faith (and bear in mind that I am not speaking of religious faith exclusively) tells us that we should treat them equally nonetheless. So we act as if it were true.
Actually, logic, reason and math can justify that too, at least if you're willing to go on semi-higher levels of it.
In game theory, tit-for-tat is a really powerful strategy for iterative prisoner's dilemmas. Basically, you co-operate on your first move and then repeat the other players move. It's the way most of us interact in life. You might smile and greet a person and voulenteer to help him, and if goes on the aggresive you defend yourself in any way possible (and I'm scaling this down to even minor things, such as gossip, where you would try stop helping a person who's slandering you slander you).
You can also use knot theory to explain why we should all be treated as equals. Robert Aumann, Nobel Laureate in economics, used it to explain that in a working knot between two ropes they are all "under" and "over" each other the exact ammount of times. Likewise, a
sustainable relationship between people needs to prioritize both parties conditions equal ammounts of times.
You can use game theory for much, much more when it comes to explaining moral behaviour than any other mathematical branch though, especially when you read papers about it being applied to auctions, and you can also use first and second order logic in order to see why stereotyping is an absolutely horrible way to deal with classification if math isn't your thing.
Basically, my argument can be boiled down to a single point: reason deals with what is, while faith deals with what should be.
I don't agree. Faith basically states what something should be and than doesn't have to give any arguments, because otherwise it wouldn't be faith. That's really bad. Faith is something that's required to explain what is, and we want as little as possible while we're doing it.