If a person stops doing the bad action or begins to do the right action, why does he still need to do Teshuvah for a חטא (sin)? In other words, why do you need to do Teshuvah if you have stopped the behavior?
Based on the Rambam, Hil. T'shuva, T'shuva is commonly broken into four parts.
So, you are talking about phases 2 & 4. It's not exactly that one still has to do T'shuva after stopping the behavior, but that stopping the behavior is part of the T'shuva, the T'shuva, however, should be complete.
The Alter Rebbe of Lubavitch in Igeres Hatsheva Perek Aleph (based on Sanhedrin 34b, and Shulchan Aruch Choshen Mishpat Siman 34) defines the mitzvah of Teshuva as the abandonment of sin; that is the sincere resolution never again to violate Hashem's will. As far as that goes, if you have stopped the behavior that is considered the Teshuva.
However that this is only in terms of the mitzvah of teshuva, not the concept of Teshuva. One who G-d forbid sinned needs to rectify the spiritual damage caused by his misdeed, and repair the severed connection to Hashem. As the Alter Rebbe explains at the beginning of the chapter, when one performs a positive command he not only fulfills Hashem's Will, but also draws down a flow of Divine light into the higher spiritual realms and upon his own soul. If one neglects the positive command, that spiritual light is lacking. Transgressing a negative commandment blemished the individual’s soul and the celestial realms. Teshuva is the process of repairing this.
[Additionally, the Alter Rebbe explains in Perek 29 Tanya that Teshuva is an ongoing lifelong process. Dovid Hamelech said "וחטאתי נדגי תמיד", "My sin is constantly before me." However, Dovid was a Tzadik Gamur who also said "ולבי חלל בקרבי", "My evil impulse is as if dead within me" (Rashi). Why was it necessary for him to constantly bear in mind his past sins? The Alter Rebbe explains the greater one's stature, the higher the level of repentance is required of him. Thus even if he may already have repented sincerely, when he ascends to a higher level he requires a higher level of Teshuva to rectify that same sin.]