Anger
The Gemara (Shabbos 105:) teaches, "If a person rips his clothes due to anger, or if he breaks an item due to his anger, or if he throws away money because of anger, consider him as though he worships avodah zarah. Because this is the technique of the yetzer hara. Today he tells you, 'Do this,' tomorrow he tells you, 'Do this,' until he tells him to worship avodah zarah, and he does so."
Anger is like serving avodah zarah for two primary reasons. One reason is that he wouldn't have become angry if he believed in Hashem and His hashgachah pratis. Also, anger is like avodah zarah because, as the Gemara says, the yetzer hara draws him from one sin to the next until he reaches avodah zarah. And it all begins with anger.
Anger Leads to Sin
The Gemara (brachos 29:) states, "Eliyahu [HaNavi] said... 'Don't become angry, and you won't sin."
The Maharsha explains, "The yetzer hara works in professional ways to lead the person from a small aveirah to greater ones... When one rips his clothes in anger, he has transgressed the aveirah of baal tashchis..." This aveirah leads to other aveiros until he worships avodah zarah.
The Meor Einayim (Brachos) writes, "All aveiros that a person does on purpose, chas v'shalom, are because he became angry. This is because every Yid has a spark of holiness in him, a part of Hashem, so how does one come to commit aveiros and rebel against Hashem? By becoming angry. Anger causes the Shechinah to leave him. The holiness leaves him, and now he can commit aveiros. This is the reason an aveirah done on purpose is called מזיד. It is from the word (Bereishis 25:29) נזיד יעקב ויזד, 'Yaakov cooked...' The word ויזד of מזיד means to cook, and it is indeed his hot and cooked-up attitude which causes him to perform aveiros במזיד, on purpose."
So, anger leads to aveiros, which lead to avodah zarah. The Gemara gives one example of baal tashchis, but there are several others. And each aveirah gradually leads the person to worse aveiros until the yetzer hara incites him to worship avodah zarah, r'l.
The Rambam (Hilchos Deios 2:3) writes, כל זרה עבודה עובד כאילו הכועס, "Whoever becomes angry, it is like he worships avodah zarah." The miforshim (חיות ץ"מהר) ask that the Gemara states that anger, together with breaking something, is like avodah zarah. It doesn't say that anger alone is like avodah zarah.
Perhaps the answer is that anger will undoubtedly lead to other aveiros. The Gemara gives an example of baal tashchis, but there are other examples. One sin leads to the next, and there is no knowing how far he will fall.
