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Do you separate? That's the key to going natural. If you just don't touch them at all, they will congo together to form one giant matted lock. It sounds like that's what you're doing. Grab hold of 2 that are connected and lightly tug them in opposite directions until they rip apart. It can be uncomfortable. Most will recommend doing it right after you wash them when they are still wet. That seems to be the easiest and least painful time for most people here. If you just washed and you don't want to wait a few days till you do again, you can always just do it when their dry. but keep it up. After every 2-3 washes normally. After each wash if you hair knots up really quickly.
Don't brush them out. This is what they are supposed to do. Mine are 5 years old, and the roots still tangle together once in a while. Not as often as when they are young, but still sometimes
If it's absolutely necessary, you can get a razor and take a small slice, then try to rip it the rest of the way. if it still doesn't rip, take another small slice, and try to rip it.
But that is in extreme cases. Have you tried using any oils to loosen up your hair and then ripping it? Aloe Vera would be good for this too. I'd try either one of these before the blade