I like your question!
Well, from my understanding, contraceptives don't necessarily inhibit ovulation. Rather they alter the menstruation cycle by changing the uterus lining or endometrium via a combination of estrogen and progesterone.
Secondly, Luteinizing hormone and Follicle-stimulating hormone induce ova-growth, NOT ovulation. So if Estrogen is taken, as you know, it will inhibit LH and FSH production in pituitary gland, and so ova-growth will be inhibited.
Estrogen, on the other hand in addition to inhibition of LH and FSH, INDUCES ovulation. Simply put, Estrogen tells the ovaries that it is enough of growing and it's time to ovulate. If it still doesn't make sense to you, go figure out WHAT makes the Estrogen.
FSH and LH induce Estrogen production! You probably know how skeletal muscles work, right? In opposing pairs. Almost all hormones work the very same way. That's how Estrogen, LH, and FSH work together; like a muscle.