Many spiritual/psychological paths (especially Buddhism and Hinduism) claim the self makes us unhappy. They don’t deny the bare fact of our existence. Rather, they claim that what we normally think of our “selves” are merely transient mental phenomena, and when we cling to them, we suffer.
It’s natural to wonder why this self is such a problem. If we take Buddhism’s focus on suffering as a starting point, we can try to work it out logically: We can infer that for “me” to suffer, there must be a “me” in the first place; therefore, removing “me” removes the necessary condition for suffering to occur and hence removes suffering. Likewise, if one equates thwarted desire to suffering, one can use a similar argument on the self’s centrality with respect to desire.
Admittedly, this is a bit simplified, and I won’t discuss the feasibility or desirability of this approach. Rather, I will invite those who want a more systematic, non-ideological, secular treatment of the problem to read The Curse of the Self. This book goes into detail about what this “self” is, the many ways it hurts us, and ways of overcoming it. I’m still reading it, but what I’ve read so far is enough to recommend it.