Why non-self instead of self is a characteristic of existence?

Question:
http://uk.answers.yahoo.com/question/index?qid=20130305132445AAYix3A

Why non-self instead of self is a characteristic of existence, according to Buddhism?

Three characteristics 'tilakkhaṇa' of existence (shared by all sentient beings) are:
1. impermanence (anicca);
2. suffering or unsatisfactoriness (dukkha);
3. non-self (anattā)

Worldly beings are subject to and also practically experience impermanence 'anicca' and suffering 'dukkha' characteristics of existence, even within lifetime.

They also live with belief of self (example: myself).

Then why non-self (instead of SELF) is considered as a characteristic of existence?

Additional Details

@Seyfert,
existence (continuous births and deaths of self) in Buddhism does not narrow to 'myself' only.
This question is a very tricky point, only a sharp mind can answer.
Please check my comment at:
http://uk.answers.yahoo.com/question/ind…
non-self is one of three characteristics of self (worldly existence)
Otherwise, 'tilakkhaṇa' should have been 'dukkha', 'anicca' and 'attā'.

Buddhism states characteristics of any worldly existence/being/self, and not just the notion of myself.
Ignorance forces a being to justify sukha, nitya and atma to motivate to regenerate self (continue existence).
When true wisdom examines the characteristics of self existence as it is, the regenerating process of self ends, meaning freedom (nibbana).

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