When the Soviets went to Afghanistan Why did other countries help the Afghan rebels if the government of Afghanistan at the time asked for its help?

In reality the "legal" Afghan government (asking for the help of the Soviets) was the result of a "Coup" led by the local Communist Party to install a kind of extreme Stalinist government that wasn't very popular and produced widespread rebellion (in particular among the most conservative fringes of the population that were against any kind of modernization/emancipation). Not only this, due to the incapacity and ineptitude to deal with the rebellion, soon the government experienced internal fighting and the original president was killed.

The leader of USSR (Brezhnev) sent the army to 'help" Afghanistan and placed a "friendly" president in charge (Babrak Karmal).
So, you could say that, as usual, a puppet government called for help to maintain his power producing a civil war.

You have to remember that at the time the "Cold War" was in full swing and the two superpowers (the US and USSR) were fighting each other through the use of smaller countries used as pawns in a bigger chess game.

Exactly as in Viet-Nam where the USSR supported the North Vietnamese against the South and the US, in Afghanistan the US supported the rebels (Mujahedeen) against the "legal" government and the USSR.