Why would Diffie-Hellman Group 21 be 521 bits rather than 512? Diffie-Hellman groups tend to increment in key sizes as you'd expect up until group 21. Any idea why the key size is 521 rather than 512? I haven't been able to find an answer at all.
"Group 21" was originally used by IKE to refer to a specific elliptic curve group, which happens to use $2^{521}-1$ as the prime modulus.

Your question is "why did they use $2^{521}-1$ is their prime, rather than a prime closer to $2^{512}$?

Well, it turns out that using $2^{521}-1$ is more efficient than a slightly smaller prime.  Most of the time implementing elliptic curve operations turns out to be performing modular multiplications, that is, given $a$ and $b$, compute $a \times b \bmod p$.  There are some tricks we can use for $p = 2^{521} - 1$ that aren't available for $p \approx 2^{512}$ (specifically because of the special form of $p^{521}-1$ as a Mersenne prime); and so they just took advantage of it.

There are no similar Mersenne prime circa $2^{256}$ or $2^{384}$, and so a similar trick was not available for the smaller Elliptic Curve groups.