Why drinking on the plane gets you drunk faster?

Because you are usually drinking on an empty stomach. There is a widely-held belief that the altitude is an issue, but the pressure altitude of a airline jet's cabin is held at a minimum of 8000 feet above mean sea level. That is not sufficiently low air pressure to affect your level of intoxication. It would require a cabin altitude of 12 - 14,000 feet to have a noticeable effect, and at that pressure altitude everyone would be getting headaches. That's why the pressure is kept at 8K, along with the fact that lower pressures could precipitate other problems.