why don't big airplanes use DC electricity?

There are two problems with DC that are rarely discussed but very important.

1 - Electric arcs. If you interrupt by accident a very common level DC current (like 5 to 10 Ampere) from a circuit with a feeding voltage over 50 Volt, the result is nearly always an electric arc (a continuous spark) that is very hot. It can burn people or set fires easily. So if you have a plug that is “lose” inside the power outlet, or if a cable brakes suddenly, the risk of hurting people or setting fires is immense (in AC the current passes trough zero 100 or 120 times per second, so most of time this arc is extinguished naturally in a matter of miliseconds). The only way to overcome this problem is working with very low voltages, but it is not practical because the feeding cables must be too thick.

2 - Electrolysis. In AC, the average voltage is zero (the positive and negative parts of the cycle are equal). Electrons and ions have no reason to move far away in one specific direction in AC, because they are attracted and repelled equally. In DC they do, and the constant flow of ions from the conductors will erode almost any connection in contact with water containing minimum amounts of salt, acids or alcalines, causing bad contacts in the long term (and bad contacts generate many problems in electric circuits).

These two issues are the main reason why even in big airplanes the power for subsystems is transmitted by AC circuits.