Quote from Jhfffan >>

Right, but why say "on any of your turns when your beast companion doesn't attack..." and follow it by "...on its turn..."? If it doesn't attack on your turn anyway, why make that distinction?

Because you can use your action to make it attack. It's just preventing giving the beast two commands in one turn.

I think technically you could still give two commands in one turn, just neither of them could be the Attack command. Almost like a Cunning Action ability.

Which is fine, but why not say "...that you don't command it to do something with your action" or something similar, or if the two commands aren't the issue "...that you don't command it to attack"?

Granted this wouldn't be the first time that the verbiage used was strange. 

This is just speculation, it would allow something like:

Bonus action Disengage, move and the action Help against another target that is more pressing.

but not allow you to do something like:

Move, bonus action Dash, then Action attack.

Basically they wanted to give the Ranger a bonus action ability, but felt it was too much to let the Beast also bite someone in that same turn. I don't really know the logic.