It is true that belief in oneself can be empowering, and that this belief can lead to positive change. However, believing in oneself and believing in one's existence are two different things. What Nikhil implies is that despite the fact that believing in oneself may be "true" in a hollow sense of the word, the fact of existing itself can't really be proven and thus should not be taken as an absolute truth.
The retort to the retort would be that while believing in one's existence is an important part of psychological well-being and taking meaningful action in life, it cannot discount the fact that existence itself is, at its core, a lie. The idea of existence is something we can never fully prove or validate logically. To believe otherwise, then, is to believe a lie - to deny Nikhil's premise would be like trying to deny that 2 + 2 = 4 - it may seem true but it cannot be proven as such. To deny Nikhil's conclusion, then, would be like trying to prove never-ending pi - impossible, and an exercise in futility. UrRong!