Let's cover all points one after the other - 

Various Systems of Astrology - As we are aware that there are many different streams of Astrology. Vedic is most commonly referred to but we all know that Western Astrology has its own rich history. There are Chinese, Japanese, Greek and many different streams of Astrology. I can easily say that we can find as many streams of Astrology as we have countries in World. I have even read Articles of Islamic Astrologers although the most popular view says that Islamic Countries don't follow Astrology. Nothing against those nations but I am just saying that how misinformed we are? Even in one system of Astrology, we can find various streams of Astrology like in Vedic System, we can find Parashara, Jaimini & Bhrigu Jyotish etc. I am sure that other systems will also have its own streams. And having so many streams just show that how much creative and innovative humanity has been. Kudos to all those people who refused to follow the past and started their own system. 

Various Charts - Indian System of Astrology becomes rich due to the existence of various charts. Besides Birth Chart, there are Divisional Charts, Bhav Chalit Chart and Transit Charts etc. As far as my knowledge is concerned, I don't think any other system of Astrology uses these many charts. But having so many charts lead to confusion as to which chart to follow and see?

Various Ayanamsha - Ayan means the Direction. So, Ayanamsha means the calculating the right direction of planetary position in a given time. There are many Ayanamshas used to calculate Birth Charts and Transits. Most popular being Lahiri Ayanamsha and the latest developed by Ernst Wilhelm, as per my information. Other Ayanamshas were developed by great Astrologers of different times such as Sri BV Raman and Sri Yukteshwar Giri etc. So which Ayanamsha and Calculations are more accurate?

Various Dashas - Another place where Vedic System of Astrology is rich is Dashas. Dashas are great tools to predict things more profoundly and accurately. But again, options lead to confusions. There are so many dashas, i.e. Vimshottari, Yogini, Chara, & Lal Kitaab etc. Most commonly used is Vimshottari but does it mean that it is most accurate?

Most Accurate System - Now, we come to the main question that which is the most accurate system of Astrology? Also, why every Astrologer says that system he follows is best and most accurate?

So, if you are using a particular System/Stream, Dasha, Chart or Ayanamsha from a long time and it has given you good results, as in correct predictions, for a long time, then don't bother about which system you are using. It is best for you. Your eyes are set on that system. Now, changing to a new system means starting from 0 again. Like, I have done consultations on over 1000 charts using Parashara System, Lahiri Ayanamsha, Vimshottari Dasha and D-1 chart alone (as most of you know that I rarely look at D-charts). So, this system and ways are perfect for me now. I have given correct predictions consistently on the basis of these things. Now, if I change it to Jaimini or Bhrigu or their respective dashas then again I have to start from 0. I will again have confidence in new system after reading at least 250 charts and after giving some correct predictions consistently. So, that's why, once you are set in one system of Astrology, continue it. Change only when you feel that there is need to change, not just because some other fellow follows a different set of rules. 

At the same time, it doesn't mean that we should not learn about different systems and concepts of Astrology. Knowledge gained will never be wasted. It is funny but I have seen Astrologers who follow Western Charts, Vimshottari Dasha and Sidereal Transits. They can give great predictions using these 3 different systems at the same time. It only means that their eyes are set on this way of predicting and they have confidence in this system. Last thing you want as a client is to go to any Astrologer who doesn't have confidence in his ways, tricks and predictions. 

So, it is not about Ego, though I accept that We Astrologers sometimes display the highest ego, but it is about having faith and trust in a system which an Astrologer follows. But yeah, if any Astrologer says that only his ways/methods/tricks are correct then it is an egotistical statement. 

Conclusion - This World, People and Life are Grey. It is neither black nor white. Everything good has some bad attached with it. My biggest enemy is someone's best friend. The person whom I may curse everyday is also getting blessed daily by someone. Nothing is completely perfect or completely wrong. Likewise, every Astrology system will have some advantages and some drawbacks while using. Like, I told you that Vedic System is rich as it has so many options of charts & dashas etc but majority of time it leads to only confusion. System is rich but we are not capable enough to handle that richness. Today only I came to know that Western Astrology has far more aspects than Vedic System. It doesn't make anyone a winner or other a loser. As I said many a times, all these different systems, tricks and ways of Astrology are here to co-operate and make our lives easy, and not to compete with each other. It is for us to make good use of all knowledge and utilize through a system which best suits us.