It's awfully difficult to say what someone's motives were, especially when all their writing is lost. Sulla wrote a bit himself, but we didn't bother preserving his account, and any attempt to get at what the hell he thought he was doing will be just speculation. There are people who make an attempt - Keaveney's The Last Republican is a fairly sympathetic biography of Sulla. It's decent, but Keaveney seems to think Sulla was some sort of religious mystic. He plays down Sulla's viciousness probably too far.

There is a case to be made for Sulla, whether it is the case he relied on or not. Sulla was the elected consul of the Roman people, chosen through the vote of the centuries. The centuries represented, essentially, the Roman army in theory if not always in practice. For Marius to transfer the Asian command to himself through a lex was a violation of the mos maiorum. It's as if Congress passed a law that declared Obama was not Commander in Chief. Marius started a constitutional crisis.

It's worth noting that Sulla's soldiers were with him, whatever reasons he gave, while his officers with only one exception refused to participate in his first march on Rome.

Julius Caesar does offer a similar justification for his march on Rome in 49. He has two casus belli: The Senate whipped a tribune of the plebs and drove him out of the Curia, a violation of the office, and by passing the SCU diminished Caesar's dignitas, which was in itself an insult against the Roman people.