Shlomo Hamelech says in Koheles; "טוב אחרית דבר מראשיתו" (קהלת ז', ח'). Simply, this means that the end of a matter is better than its beginning. However, it could also be interpreted that the end result of a matter is dependent on its beginning. This means, if the outcome will be positive or not, is mostly dependent on whether it had a good start at the beginning. Thus, when beginning something new, it is important to start out on the 'right foot', since the way one starts out affects the conclusion.
This point is clearly illustrated in the story of Elisha ben Avuya, better known as Acher.
Chazal relate that Elisha ben Avuya, who was the rebbe of the great Tana Rebbi Meir, strayed from Yiddishkeit. Because of this, he is often referred to by Chazal as אחר, the other one, symbolizing that this is a different persona. Once, while riding a horse on Shabbos with Rebbi Meir escorting him, Acher turned to his talmud and told him that he should not continue walking because he has calculated that they are about to cross the techum. While he was saying this he was deliberately continuing on his way, proceeding to cross the Techum Shabbos. Seeing this, Rebbi Meir suggested that his rebbe 'turn back', both literally - by coming back into the perimeter of the Techum - and also to return to the Torah way. To this, Acher replied "I heard an announcement from behind the Curtain in heaven that said: 'return, all rebellious children of Hashem, except for Acher' ". In other words, Acher was saying that he is too far gone for his Teshuvah to be accepted on High. Thus, as much as he would like to return to Yiddishkeit, he can't, since Hashem had explicitly stated that he is not welcome anymore (חגיגה דף ט"ו.).
The ירושלמי adds that Rebbi Meir further insisted that Acher do Teshuvah, quoting the aforementioned pasuk "טוב אחרית דבר מראשיתו", the end of a matter is better than its beginning. Rebbi Meir was trying to impress upon his rebbe that although he has stumbled, if he were to come back, he could attain a greater level than before, and ultimately rank higher. Acher, however, interpreted the pasuk differently; "טוב אחרית דבר", the end of a matter could be good only if "מראשיתו", it was good from the start. Thus, claimed Acher, since the beginning of his life was not good, he would not do Teshuvah, as he anyway stood no chance of becoming better.
Tosafos explains what Acher was referring to by saying that "his beginning was not good", by citing a story that took place at the Bris Milah of Acher. The Tano'im Rebbi Eliezer and Rebbi Yehoshua had come to take part in the celebration of the Bris. At one point during the seudah, they got into an animated Torah discussion. Suddenly, while they were talking, a fire surrounded the house. Afraid that disaster was imminent and he would lose his possessions, Acher's father Avuya asked them "have you come to burn my house down"? The Tano'im replied that there is no need to worry, this fire will not cause damage; the fire was only generated because they are exchanging words of Torah in a way that brings such joy similarly to the when the Torah was given at Sinai through a fire. Thus, the fire that had enveloped the house was of a spiritual nature and would not incur any damage. Amazed and inspired, Avuya exclaimed: "If the power of Torah is so great, I wish to educate my newborn child to a life dedicated to it". Tosfos concludes that because his father did not dedicate him to Torah with pure intentions, l'sheim Shamayim, it did not stand him in good stead in his future life.
Additionally, the Yerushalmi relates that once on Yom Kippur an expectant woman smelled food and got craving for it. People tried easing the temptation by whispering in her ear that it was Yom Kippur. This was ineffective and, being unable to calm her desire, she ate. That child later became Acher.
Thus, when Rebbi Meir suggested that his rebbi return to the Torah path, Acher objected, stating that the beginning of his life had started out wrongly - his mother ate on Yom Kippur and his father's intention of dedicating his life to Torah was not totally l'sheim Shamayim - hence he believed there was no hope for his future. Moreover, Acher argued that Hashem was not interested in him, since he had heard an announcement from Heaven inviting everyone to do Teshuvah, but explicitly stating that Acher's Teshuvah was not welcome.
This highlights the great power of starting something new, for within the beginning lies the possibility and potential for success throughout the endeavor one is commencing.
Alternately, many of the ספרי הקדושים say that if Acher would have persisted, his Teshuvah would have surely been accepted by Hashem, for Chazal say "אין דבר העומד בפני התשובה", there is nothing that stands in the way of Teshuvah. Rather, the Bas-Kol was implying that since he had stooped so low, he did not deserve to merit the Divine assistance usually granted to one who does Teshuvah. As such, Acher 'erred' in believing that he was too far gone for his Teshuvah to be accepted on High.
However, his initial idea - that the end of a matter strongly depends on its beginning - was also true; he correctly grasped the extreme power inherent in 'beginnings'. Indeed, Rashi in koeheles quotes both interpretations. Where Acher unfortunately erred was grasping the extreme power of Teshuva.