A 21 day old wine is NOT going to taste great. Wines take time -- they undergo chemical changes that don't happen quickly.
The time frames in wine kit instructions are approximate. Yeast is a living being and it WILL do what it wants, not what you want.
As
@joeswine said, follow the instructions, keeping in mind that time frames are approximate. Your hydrometer tells you when to do the first racking.
Following is my process for kits, which should illustrate the differences in time frames. I follow the kit instructions generally, e.g., I do things in the order indicated.
I typically first rack at ~1.010. This has been as short as 4 days and as long as several weeks, but is generally 5 to 7 days.
From there it goes into a carboy to finish fermentation. For red wines, the SG should finish between 0.990 and 0.996. I typically wait a week before checking. IME the wine will normally be done fermenting by this time. If it's not, give it another 3 to 7 days and check again.
Rack again to get the wine off the gross lees and add the fining agents (typically kieselsol/chitosan in kits). I typically rack again in a week or two. This depends more on my time than the wine, but in general I want the wine off the lees sooner than later. During days 2 to 4, give the carboy a sharp twist to dislodge sediment from the sides -- this reduces fine sediment in later rackings.
In theory, a 28 day kit can be bottled 2 weeks later. You DO NOT have to bottle, and I can't recall the last time I bottled a kit "on time". Some folks age kit wines for 12+ months. While I don't see any value in that unless you're adding oak products, it's definitely not wrong to age the wine a lot longer than indicated.
After bottling, don't touch the wine for at least 3 months. In general, reds are drinkable at the 6 month mark but will be better a year out. This is personal taste -- if you like the wine at 3 months, enjoy! But put aside a couple of bottles to age a year, so you can taste the difference.