What makes birth control fail when taken perfectly? for example, with no anitbiotics; pills always taken at the same time; no diarrhea and no vomit?

Birth control failur: Oral contraceptives - birth control pills - are designed to prevent ovulation. At the currently-used doses these pills do not prevent ovulation 100% of the time. In those infrequent cases where ovulation still happens pregnancy has a chance to occur. Higher-dose pills used in the past had an unacceptable complication rate, and are not available any longer.

Not always clear: No bc method is perfect--possible factors: there are undoubtedly some factors related to metabolism (fast or slow) or so that low dose pills might not be strong enough to suppress ovulation.In addition, being off of hormones for 7 days of placebos may allow the ovaries to escape their suppression (or "wake up"), possibly allowing ovulation. So 4-5 days off, or continuous may be more effective.