Question

What ideas did luther teach that put him at odds with the pope and the church?

Answer 1

Luther is famous for his 95 Theses of October, 1517, in which he argued against the church's sale of indulgences.  Indulgences were papers from the pope that offered people release from penance they owed for their sins. These theses put him at odds with the pope and the church because indulgences were a major source of church income.  Luther argued that if the pope really had power to remove people's penalties for sin, he should do so freely for all.
Several weeks before the famous 95 Theses against indulgences, Luther had writted "A Disputation against Scholastic Theology," a set of 97 theses aimed at the core teachings of the Roman Catholic church's main theological scholars.  After the controversy over indulgences got started, Luther was called upon by his brothers in the Augustinian order of monks to defend his theology.  In doing so at Heidelberg, in 1518, Luther spoke more fully about the central problem's of Rome's theological system.  Throughout his career, Luther continued to attack the system of Roman Catholicism which had people earning their place with God on the basis of merits, penances, pilgrimages, etc.  Throughout his career, Luther's emphasis was on salvation by grace alone, coupled with a rejection of Rome's system that portrayed God giving rewards to the acts we do by our own wills.  This is what most put him at odds with the church's teaching.

Luther also went as far as to call the pope the Antichrist because he saw the office of the papacy getting in the way of the gospel of Christ and claiming authority for a human leader that only Christ himself should have.