It's supposed to be a covenant, right? Shouldn't a *grown man* make that decision for himself? FORCING a helpless baby to make deals with the almighty creator of all existance when they're incapable of exercising their "free will" and making that decision, and then on top of it hacking on their dicks when they can't defend themselves... It's, umm.. Well, weird. Really, REALLY weird. 
Well like you said it was part of a covenant with God, but it's really not that weird. I don't know where you live but there are TONS of people in America who were circumcised as babies with no choice but the choice of their parents.
Yes, it IS weird. YOU'RE CUTTING PIECES OFF A BABY'S DICK. WITHOUT IT'S PERMISSION. FOR RITUALISTIC PURPOSES!!!
In what possible reality is that NOT weird!? What is wrong with you!!??

I'm AWARE it's very common. But you're totally ignoring what I'm asking. You're instead telling me what I already know.
*What kind of God asks such a thing? Would YOU ask such a thing of somebody???
"Hey Marty. I know you said you'd help me move this weekend... But I'm gonna need you to go ahead and slice off the tip of your penis to know you're serious."???? I dunno man. Sounds like ancient bronze-age desert dwelling goat-herder superstition to me. And not so much the mandate of some perfect, all powerful, timeless deity.
Especially when you throw in all the other stuff about goats, animal sacrifice, slavery, virgin-sold-to-her-rapist policy, etc.
*Where does that child's "free will" come into play? He has no choice in the matter.
I would put forward that it's done this way because the clergy knows that if they DID wait until the child was old enough to make this decision for themselves, they'd see one DRASTIC drop in church attendance. See, according to your religion, it's *required*. But very few sane person would volunteer for such a thing. Only the MOST devote bible beater would do so.
So what do you do? You do it when they're defenseless INFANTS with no say in the matter.
Real classy.

If you are a god, and it's SO important, and you have no intention of giving the individual a choice in the matter, why not just snap your fingers and change the human genome so that foreskins just <POOF!> dissapear from Christian peni? Why put it in the hands of the parents?
What possible PURPOSE does it even serve? It's supposed to be this big agreement between god and man, but it's done (as I've said, MUST be done) before the person even has the capacity to understand the magnitude of the arrangement.
I'd further suggest that having to make the choice YOURSELF, as a young adult, would be in every possible way more effective in ensuring the individual remembers the alleged importance of it.
Seriously. I want you to think about this. Aside from physically branding you as a Christian/Jew for LIFE, and aside from the fact that the overwhelming majority of young adults/adults would leave the church altogether before volunteering for such a thing, it not only serves literally no purpose what-so-ever to do it when they're a baby, but it effectively removes all meaning from this so called "covenant", since it's not so mch a "covenant" as it is a FORCED practice on a defenseless baby.
*If a religion popped up over night that encouraged anally violating an infant with a piece of religious iconography during some bizarre ritual, and "TONS of people" started doing it to their kids... You wouldn't think that's a little WEIRD to say the least?
And anally violating a baby is no worse than, again, CUTTING PIECES OFF OF IT'S GENITALS. It's the exact same level of sick. Yet you've been told by your religion that there's "nothing weird about it", and never questioned it. That would bother the hell out of me if I were you.