Luther didn’t split.
He tried reform and the Catholic church ex-communicated him for his trouble.
In Canon law, excommunication is a "medicinal penalty" intended to invite the person to change behavior or attitude, repent, and return to full communion. It has sometimes imposed illegitimately (since human beings are sometimes unjust!) but, more often, rightly and lawfully. Excommunication does not "undo" membership in the church; excommunicated Catholics are still Catholics, not banned from the assembly, not banned for instance from Mass, but still under the obligation to attend Mass (!) though not to receive Communion.
Not a few saints, later canonized, were excommuncated for some period in their lives. Examples are St. Hippolytus, St. Columba, St. Athanasius (yes, that Athanasius), St. Joan of Arc, St. Hildegard of Bingen, and St. Mary Mackillop. Athanasius and Hildegard were certainly reformers, and are now considered Doctors of the Church.
I think Luther's chosen course was to defiantly blow up his excommunication into a permanent rupture. Both the "Pope" side and the "Luther" side made errors of judgment; his was his decision to, as I said, split. And of course, writing pamphlets urging German princes to take up arms and make war on the Church and on the peasants was a definite no-no.