If someone tends to be hypercritical and find fault with everything, you can describe that person as captious. Try not to be described as a captious person yourself, however. No one likes a carping individual!
Captious comes from the Middle French word captieux, which is from the Latin word captiosus meaning fallacious or deceiving. This is, in fact, another meaning for the adjective captious, something is calculated to confuse or deceive — such as a captious explanation of the facts. When a person is described as captious, the sense is usually of nitpicking at faults or raising petty objections. It is usually used to imply a permanent character or personality flaw, as opposed to a momentary lapse in understanding.