Reasons for Chinese SM2 Digital Signature Algorithm
The SM2 digital signature algorithm.  Fix a curve $E/k$ over a field $\mathbb F_p$.  Fix a standard base point $G$ of prime order $n$ on $E/\mathbb F_p$.  Fix a hash function $H\colon \{0,1\}^* \to \mathbb Z/n\mathbb Z$.


A public key is the encoding of a point $P \in E/\mathbb F_p$ together with an string $Z$ identifying a principal.
A signature on a message $m$ under the public key $P$ with identifier $Z$ is is a pair of integers $(r, s)$ in $[1, n - 1]$ such that $r + s \ne 0$ and $$r \equiv (H(Z \mathbin\| m) + x([s]G + [r + s]P)) \pmod n.$$
The signer knows the secret scalar $d$, the private key, such that $P = [d]G$.  To make a signature, the signer picks a scalar $k$ uniformly at random, and computes

\begin{align}
    r &amp;\equiv (H(Z \mathbin\| m) + x([k]G)) \pmod n, \\
    s &amp;\equiv (k - r d)/(1 + d) \pmod n,
  \end{align}

rejecting and starting over if $r \equiv 0$, $r + k \equiv 0$, or $s \equiv 0 \pmod n$.

This is a valid signature because

\begin{align}
    [s]G + [r + s]P
    &amp;= [s]G + [(r + s) d]G \\
    &amp;= [s + s d + r d] G \\
    &amp;= [(1 + d) s + r d] G \\
    &amp;= [(1 + d)(k - r d)/(1 + d) + r d]G \\
    &amp;= [k - r d + r d]G \\
    &amp;= [k]G.
  \end{align}


Why?  There has been relatively little analysis of the SM2 signature scheme that I can find in the anglophone cryptography literature beyond some side channel attacks.  The most salient aspect of it to my eyes is that it is just different from various other national pride digital signature schemes.

The SM2 signature scheme has a small advantage over ECDSA (US) and ECGDSA (Germany) for verifiers: the verifier need not compute any inverses modulo $n$.  Otherwise the signer's costs are similar to the others.  Security analysis of ECDSA is extraordinarily complicated and unsatisfying, in contrast to Schnorr; I expect the same is true of the others.

My guess about why SM2 was chosen is precisely to be different from all the others, for the sake of nationalism—they are all worse in performance and confidence than the much simpler inversion-free Schnorr-based EdDSA.