Chickens get tougher the older they get. Many people think that is due to how they eat or something else, but I think it is mainly that they age.
The chickens you are used to getting at the store are are 6 to 8 weeks old and very tender. Yours will not grow fast enough to butcher at that age unless you are happy with very little meat. People butcher quail and an 8 week old chicken is bigger than a quail so if you want to butcher it then you can, but there really will not be much meat.
Chicken, whether hen or rooster, also develops more flavor as it gets older, not just get tougher. Some of us like that. Some don't. You cook different aged chickens differently to take care of the toughness issue. Flavor, well, that is just your opinion which may be different than mine. A properly cooked chicken of any age can be very tender.
When can you process a rooster? Anytime you want. I usually wait until at least 15 weeks and usually wait until 18 weeks so I get more meat, but I have processed and cooked very mature roosters and they have turned out very tasty and tender.