Alright so when using a mount we have two options: command it or let it act independently (PHB pg. 198). Letting it act independently is the only way to get it to attack, given that it chooses to attack (which I would expect it to do if it's naturally aggressive or trained for combat). So if you have a warrior of a mount under you, he will be attacking separately from you, essentially giving you extra attacks.
When playing the Beast Master Ranger and using its animal companion however, we can only command it (PHB pg. 93). Letting it act independently is absent from the RAW and as such, it is not possible to have it attack without wasting your own attack on it. So, essentially, you're not gaining much other than versatility and range. You are not getting any extra attacks.
So, in my desperate efforts to care about the beastmaster class, I hatched the following plan. Play a small race. Make a medium creature your companion. Mount it. Let it act as an independent mount. Independent mount does whatever it wants, hopefully it wants to attack.
This would mean giving up on Bestial Fury (which lets the companion attack twice but only if you specifically issue the attack command), but that doesn't matter.
My question is can you let your companion mount act independently or do you have to use the Beast Master's commands to control him?