Why do lag when someone else is playing?

Get better internet would be the only real way to do it. Contact your provider and see if there's a higher plan, have them check the internet line, modem and or router. The line, modem and the router can malfunction and cause internet speed to go down. Check what your provider says your speed for downloads and uploads should be and use speedtest.net to check the speeds. Above all let them know about the speed difference when he plays minecraft and you are trying to use youtube.

Umm can you explain a bit more? From what I understood, your brother doesn't lag when he plays minecraft and youtube but when you play both of them you lag? If so it's just the timing.

It's done on purpose to make people not want to play the game any more. Because if they sell a game and people do not take it back instantly then they have made their money.

The less consistent players that play, the more money the game companys make. The only solution is another system or upgrading your pc.